It's the reactions of 2019 Brits that will lead to protests if HMG makes genocidal attacks on civilian targets, so what matters is what's fresh in their memories.
I don't believe the 2019 population
would be that furious that they would topple the government. As i say, we know, in 2019, quite how evil the Nazis were, in a way which only came out after the war, in the likes of the Nurenburg Trials. Using weapons against them is not IMO going to bring down the government. Should teh government wish, it can do a massive PR blitz prior to any attacks to make sure the population are reminded of the Nazi crimes, the consequences of defeat and to remind that we are in a Total War situation.
Certainly, efforts should be taken to minimise civilian casualties
where possible, so perhaps don't take out the centre of Berlin, but given that nuclear weapons are, at least at the start, the uptimers only trump card, there is no avoiding there use at some point.
Easiest thing to do. Start off with a threatening demonstration-say off North Sea Coast, or an area of mass concentration of German forces outside urban areas.
Then take out a location personal to Mr H such as the Wolfsschanze
Should that fail to result in a surrender within X amount of days, take out a major transport or industrial hub (one which cant be readily moved or dismantled at short notice). Even give a warning, and recommend they move the civilian population.
If this doesn't result in a surrender, you then have no choice. Chose the weakest nuke you have. Pick from a major urban centre of political or economic importance, and bang.