how can he be PM unless he is willing to push the button?
Heaven help us if it comes to that. A nuclear strike would be devastating to the whole world, not just the recipients. A nuclear war would mean the end of the human race and most likely all "life as we know it" on this planet.
Anyone who pushes such a button, whether in retaliation or not, is committing a crime against the whole human race. Unfortunately, if it ever happens, there may be no-one left to prosecute him.