Hey, look, something else completely preposterous. What fun.
Three things, among dozens, are wrong with that scenario. Firstly, North Korea is situated on a
peninsula, meaning it will feel the effects of any flood much worse than a continental body. There is no way, short of an asteroid impact or a volcanic venting event comparable to the Siberian or Deccan Traps, that the caps would melt that quickly. And lastly, ignoring the fact that North Korean missiles are incapable of lofting nukes, or of doing so for the forseeable future, should North Korea for some reason attack the United States (which is itself stupid, as it would just attack
South Korea directly instead) then there would be
nothing left of North Korea to counterattack an initial American strike, nor would the American arsenal be anywhere near depleted from the effort.
[EDIT] Oh, yeah, and Cuban paratroopers. That's a pretty good joke right there. Like Ugandan ICBMs.

Radioactive ruins are a high priority for military occupation, too. How
do you come up with this stuff?