One bomb in Korea would have led to many, many more. The USSR would have jumped in full throttle.
In Vietnam,.. Well the US never really tried to fight that war. If we had treated it like we did Germany in WWII, the outcome may have been much different. Since WWII, every war the US have fought has had layers upon layers of ROE that make waging the fight very hard. And there is no cler objective on what “winning” means.
No they wouldn’t have. The USSR would not have nuked the USA if we dropped one on the gooks in DPRK.