China was not a puppet state. Mao (may he never rest in peace) was conducting his own diplomacy and his own domestic policy.
Japan was already militaristically crippled when Atom bomb was droped. Eisenhower stated the same and opposed the use of the bomb, although he was far from being a humanitarian.
War over Cuba was a direct result of nuclear missles. If soviets were not brining nuclear missles how could there have been a Cuban Nuclear Missle Crisis? By the way, American ships were attacking a Soviet submarine, - some of the crew wanted to fire back, but one of them restrained them. If the sub fired back, there would have been War. Someone in this forum posted an article on this at some earlier date.
That's just alternative history, the WWI theory. People before WWI idealized warfare much more than we do today, so we don't know what would have happened if they had such a WMD.