Some hipster picks for NZ, in roughly ascending order of difficulty and obscurity:
Winston Peters: A fairly safe bet for a 1980s POD, Winston was Rob Muldoon's protege and served as the centre-right dissident to the 1980s wave of deregulation and neoliberalism. OTL, this led to him being expelled from National and setting up NZ First, though there has long been a school of thought holding that he could have been leader had he wanted. This would probably have been more difficult than people think given the zeitgeist of late-1980s National, especially because a Winston who would've kept his head down long enough to make it far enough to be a realistic prospect for leader probably wouldn't have secured his powerbase in the first place. In a sense the trope of early 90s Tory Winston is kind of like a Labour Paddy Ashdown - a nice shock twist for a 2015-era TL, but sort of played out at this point.
John A. Lee: Yes, sound the David klaxon, it's the 1930s herald of socialism-cum-social credit. A one-armed war hero from Dunedin, Lee entered Parliament in 1922, was defeated by 37 votes in 1928 and spent the triennium managing a hotel bar in Rotorua, before re-entering in 1931 and making himself a darling of the heterodox left and an enemy of the Savage wing. This proved to be a poor career move when, in 1935, Lee was not invited to join the Labour Cabinet and instead remained on the backbenches, whence he spent the next five years flinging shit at the party exec for being a bunch of melts for rejecting his proposals to nationalise the Bank of New Zealand. Lee's attacks on the party intensified in 1939, resulting in Savage denouncing him (Lee) from his deathbed and the party expelling Lee in 1940.
Lee promptly formed the Democratic Labour Party and cleaved away a few left-Labour members, whom he promptly alienated with his abrasive style. The DLP won zero seats in 1943 (including Lee's), but drew enough of the vote to lose Labour several electorates; Lee would stand again in his Grey Lynn electorate in 1949 and come third. He continued his writing career, including a number of [revisionist/accurate/self-glorifying/vengeful] (delete as applicable) histories of the Labour Party and some quite good fiction (depending on the reader's perspective, this may be a distinction without a difference).
Lee is a slightly edgy choice who indicates a more leftist or Creditist Labour Party, though there is a sliding scale of plausibility between Lee as a Cabinet Minister and Lee as Prime Minister.
Rob Muldoon: ...wait, what?
Hear me out: Rob Muldoon was Prime Minister between 1975 and 1984 for the National Party, Think Big, schnapps election etc. etc. However, in his childhood Rob was strongly influenced by his very socialist grandmother Jerusha (because of course that's what a socialist granny was called in the 1930s), in turn helping shape his statist/interventionist approach. At the softer end of the plausibility scale, a Red Muldoon is a reasonably phresh pick for a Labour MP, though the particular circumstances that enabled him to become leader of the National Party are less likely to apply on the other side of the aisle. Maybe a Minister, depending how far you're willing to stretch plausibility from a pretty dodgy starting point.
Bob Jones: Not getting anywhere near Cabinet, let alone PM, but it's theoretically possible to get him a seat in 1984 if he manages to win a three-cornered race in Ohariu. Even that's a tall order: IOTL Jones came third, it looks like all of his support in the seat came from National vote-splitting (Labour's voteshare was consistent in the seat with the past two elections, indicating that Dunne only won by holding a pretty solid base while the Tories turned and ate each other), and it's hard to get a result that manages to be worse for National without simply pushing people to Labour.
Supposing Jones does pull through in a squeaker, it's unlikely he does particularly much once he gets to Parliament. He'll probably just amuse himself with the raised profile a seat gives him and spend three years doing some high-octane trolling (this having been Bob Jones' brand for the past 60 years). If he doesn't just up and quit partway through the term he almost certainly declines to stand for re-election, his mission of neoliberal reform having been taken up with gusto by Labour. If he does stand, he gets utterly annihilated.
Brian Talboys: Floated as the alternative to Rob Muldoon in the abortive 'Colonels' Coup' of 1980, Talboys was a kind of fallen souffle version of John Major. Minister of pretty much everything at some point between 1962 and 1981 and Muldoon's Deputy, Talboys was a fairly mainline Nat of the Holyoake consensus who appealed to the traditionalists (who by 1980 were thoroughly uneasy at Muldoon's autocratic style).
The key issue with a Talboys leadership in 1980 is that he didn't actually pursue it. There was a key period of about two weeks when Muldoon was overseas in which the plotters could have probably won enough caucus support to hold a vote as soon as Muldoon returned. However, Talboys prevaricated and simply said he'd accept a leadership challenge if his colleagues deemed it necessary; his refusal to advocate on his own behalf meant that when Muldoon got wind of the plot, he was able to seize momentum and put the fear of God into just enough of caucus to keep the leadership in a squeaker.
A Talboys premiership is therefore thoroughly achievable with that POD, but you'll need a compelling reason for Talboys to actually work for it. There's also the question of what he'll do once he wins, to which the answer is probably 'not much'. 1981 was a very close-run election for National, and it's likely that a Talboys coup just gives you a Bill Rowling-led Fourth Labour Government when Rob's Mob stay home - which I'd argue is a more interesting consequence (and have in the past).
Hugh Watt: Another deputy who didn't pull through in a leadership election, Watt was the Acting PM after Kirk died and, as Minister of Works and Electricity in the Second and Third Labour Governments, owned a lot of the industrial relationship that were a big part of the post-WWII social bargain. Despite positioning himself as the successor to Big Norm he lost to Bill Rowling in a landslide, to Watt's genuine surprise.
Getting to a Watt premiership is like playing Talboys on Hard mode: similar to Talboys, he lacked the momentum to carry the day; unlike Talboys, this was despite him actively campaigning. Much like Talboys (and Rowling IOTL), it's likely that a Watt victory is a hospital pass; the '75 election was a wipeout and the structural factors are pretty strongly against anything better than a narrow Labour loss, followed by a Rowling challenge in Opposition (which could actually put Rowling in a stronger position against Muldoon in '78, which IOTL was a reasonably narrow loss on swing seats, if he lacks the shame of the '75 defeat).
Ralph Hanan: A solid 'who dat?'; he had a neat pipe, he abolished the death penalty after crossing the floor, and he died at 60 from wounds sustained at the First Battle of El Alamein. If you need to fill a Holyoake-sized gap in the National Party between 1950 and 1970, Hanan is as good a name as any for a moderate-to-liberal choice, though he may have traded too heavily on his liberal history (to hold his purplish Invercargill seat) to make inroads with the National faithful in a 1960s POD.
However, Hanan was enough of a realist to balance the abolition of the death penalty with a tightening of penalties on crime (including *checks notes* homosexuality), so was enough of a compromiser to get things done. Overall, I reckon Hanan is a great choice for a moderate centre-right PM in the Long 1950s of NZ (c.1951-1968), with a sort of progressive 'keep an eye on those Reds' individualism that can be summed up by one of his speeches: “Liberalism, with its progressive spirit, will revive in this country, and it will defeat socialism”. Sort of Kennedy meets Wilson meets Menzies.
James Hargest: Another veteran, this one a Tory, Hargest was MP for Invercargill from 1931 to 1944, first as an independent aligned with Reform then for the newly-minted National Party, for which he was a strong advocate. After the 1938 electoral wipeout Hargest was considered a frontrunner for the leadership, but the start of WWII interrupted this as Hargest immediately volunteered for service (though he remained an MP). Sid Holland subsequently became National leader, a situation which might have been seen as temporary until Hargest - re-elected unopposed in 1943 - returned. This was firmly consigned to the realm of conjecture when Hargest stopped a shell burst in Normandy while making a farewell visit to his unit on the same day he'd been appointed commander of the reception group for repatriated POWs back in Britain.
In a TL where Hargest doesn't get killed and ends up making it back to NZ, there are a lot of potential directions. Even setting aside the conjecture that he was National's King Across the Water, Holland will have to contend with the fact that one of his returning frontbenchers is well-established as a potential competitor. Not just that, Hargest is a war hero coated in fruit salad and dramatic exploits (DSO, Military Cross, and Legion d'Honneur, WWI; two bars to his DSO, CBE, Greek War Cross, WWII), at a time when the servicemens' vote has decided one election and is about to decide another.
In addition to his WWI record, Hargest was at the time of his 1943 re-election somewhere in Occupied France with the Resistance, en route from Switzerland to the British Consulate in Barcelona after escaping an Italian POW camp (one of three Allied soldiers to manage such an escape pre-armistice with Italy). He followed this up by serving as NZ's observer at D-Day, landing at Gold Beach with 50th Division and fighting in Normandy up until the OTL shelling. There is a skeleton in Hargest's closet in that he may have been directly responsible for the loss of Crete (where he won the first bar to his DSO), but efforts to seize on that may just be seen by the electorate as sour grapes. Overall, that's a strong record to wave in front of the RSA and the Party faithful.
Hargest is something of a cipher, so he could really go any way one liked (and I've got him tagged for bigger things in some plans of mine). At the very least, he offers a change of pace from the Holland-Holyoake axis in an ATL First National Government.