In this light, I'll note that Bush the elder removed US all nuclear arms from the Korea peninsula in 1991 (although Pyongyang's certainly still in range of American missiles and bombers):
http://thediplomat.com/2013/03/not-a-good-idea-american-nuke...
Overall, my impression is that North Korea fears a conventional ROK/US invasion much more than a nuclear exchange scenario, and that this fear (rather than of American nuclear artillery, missiles, etc) has been the primary motivation behind their nuclear arms development.
I don't think a conventional US invasion is likely, hence my comment. I also don't think the situation would be different if NK didn't have a nuclear arms program, given their alliance (or subordinate relationship?) with China.