Putin should threaten to drop a tactical nuke on Kyiv in 7 days if Ukraine doesn't surrender. If they still refuse to negotiate after Kyiv is nuked then he can threaten to nuke Lviv next. This would give civilians enough time to leave the city.
The US nuked Japan twice to end a war, and that was without any warning. If Putin gave a week's notice that would be enough time for everyone to leave the city to minimize civilian deaths.
That's a bad play -- like flipping the chess board when you're winning just because you had to sacrifice your queen for an advantage. You're gonna win anyways, even if you don't like losing pieces.
You have to realize what people do when they are threatened with a no-win scenario. They go ballistic.
Even a feint threat of nuclear power isn't to be taken lightly, as the civilian populations would then scramble to flee and fall into more enemy traps and bloodshed. Stampedes are deadly for many reasons, but none the more relevant than panic and terror. Even worse is the potential of your enemy using that panic and terror against you.