I odnt believe for a second the americans would have started WW3 over Korea.
I hardly doubt that Ike would have wanted to start another world war, especially with the US and to a much lesser extent the Soviets and British having their own bombs.
That being said, despite the better information that we know of today, at the time, so politicians and generals still thought that a limited use of the bomb, ie using say 3 or 4 weapons only, could be done without starting a large broader war.
The targets would have either been located in North Korean territory or China, as despite offering supplies and advisors, dragging the Soviets into a fight would be a guarantee to escalate, regardless of what the North Koreans and Chinese do.