I don't see where I mentioned nukes but since you brough it up - you offer only one side .
You had mentioned it in passing in an earlier post. I figured that's what you were alluding to when you talk about not being able to the same for "centuries" (since pretty much no conventional weapon could do that).
If in fact a very limited nuke hit N.K. and had little if any effect on other countries it may be seen in a different light than your post cast. Consider China in the long run who will mean more to China in the long run N.K. with little economy and alot of debt or American Markets ? They may turn their heads .
Trust me, nobody would turn their heads. Whoever next uses a nuke in a military role will see the world turn on them. It's like the crazy guy who gets drunk and punches his wife at a party - even his best friends are going to jump on him and subdue him.
Back to non nuke warfare some well place attacks would take out the leadership and maybe lead to a more stable if not one Korea .
By all means, conventional, not nuclear warfare is completely called for in this context. I think eventually this conflict is going to come to a head anyways, and North Korea can't be allowed to expand into South Korean territory (more land and holdings means more resources, and we can't afford to let N Korea gain that).
I think South Korea should respond in turn. If they need our help, I think it would certainly be a lot more useful than our deployments in Iraq. The tricky part is not getting China involved. We really, really, REALLY can't afford to go to war with China. Doesn't matter which side wins that - both countries would be utterly damaged. We'd be talking a war that would likely far exceed the destruction seen in WW2.
SOMETHING does need to be done though.