I don't think Putin would have an exit. Losing the war would result in a major risk to his continued rule, and thus to his person, from a collapse of domestic support. A Ukrainian nuclear strike would present him with a choice: risk internal revolt, or risk the consequences of nuclear retaliation. I'm not remotely confident he'd choose the first. And, to be very clear, the second would make Ukraine (and likely the rest of the world) a lot worse off than they are today.