I mean, Naguib would have been viewed as an colonial puppet from the outset regardless of how he would act, merely due to the way he would be made president in the first place - by the barrel of the guns of the British and French. And that something similar was done against Urabi in the 1880s is not exactly something that would make Naguib any more popular, considering that Egyptian nationalism considers Urabi a prececessor to their ideology, and because the suppression of his revolt resulted in a continuous British occupation. Not good memories to evoke. I suspect his regime, lacking legitimacy, would swiftly collapse in the absence of British and French guns regardless of what he would do. And it would have been tough to establish a constitutional state much less a democracy, considering it would be viewed (and his OTL attempts were viewed) as an attempt to restore the corrupt elite of the Wafd era. Much of Nasser's appeal was that they cut the power of this old elite; that, as you note, he pointed to minorities and regarded them as part of this elite (some of whom really were privileged during British colonialism) was a side-effect useful for his ideology.The British, French, and Israelis - more or less - viewed Nasser as the second coming of Adolf Hitler; and anything short of his overthrow as a repeat of Munich.
The "Socialist" laws of 1952 amounted to the expropriation of businesses from "foreigner" ... meaning Greeks (350,000 to 400,000 people), Syro-Lebanese (over 100,000 at the turn of the 20th century), Jews (over 75,000), Italians (over 60,000), Armenians (over 40,000), Maltese (over 20,000), and various Europeans who lived in Egypt - particularly around the Canal Zone. This in combination is somewhere between 5% and 7% of the Egyptian population. Nasser's Pan-Arabism also excluded the Copts from being a core aspect of Egyptian identity, and they were also disproportionately affected by Nasser's anti-commercial policies, and they were another 10% to 20% of the population. So somewhere between 15 and 27% of Egypt was considered, to some degree or another, non-Egyptian under the Nasserist definition.
And Nasser was a young, charming, charismatic man who emerged from a military background; blended ideas of Pan-Arabist ethnic/racial primacy and unity, Nationalism, Socialism, and militarism together; was intent upon overthrowing the constraints upon his people who were burdened and divided by the British and French. The Munich flashbacks seem pretty understandable.
The British and French overthrowing Nasser and replacing him with Naguib also doesn't seem very different from what they did during the 1880s either.
None of this should be understood as me saying that it would have worked out had the US not told them to cut it out. I'm just trying to paint the picture of why the British and French thought it would work out well. They clearly failed to understand the amount of popular support Nasser in particular had (whereas the Ali dynasty in the 1880s was much less popular). If they'd succeeded in overthrowing Nasser, my guess is it'd have resulted in a Civil War and a split between a 'North Egypt' backed by Britain and France and a South Egypt run by Nasserists. But Naguib wanted to legalize opposition political parties (and perhaps even the Muslim Brotherhood) and Naguib doesn't seem like the sort of guy who'd be interested in being the plaything of the British and French. The only way for such an anti-Nasserite regime to have legitimacy would be (ironically?) to have the Americans force the British and French out of Egypt and restore full sovereignty over the Canal zone - such that it could paint itself as both Independent and Anti-Nasserist.
I'm not saying that Nasser was a good leader at all - he was an ethno-nationalist military dictator after all. His ideology may very well been influenced by fascism, though fundamentally he owes far more to the currents of "third-world nationalism" (for lack of a better term) that were popping up in this period. But there were reasons he was extremely popular despite that, after Suez, his career was one failure after another.