And how would you destroy them completely?
Bomb and destroy any and all vital infrastructure starting with the most vital and militarily important to them with anything we have under nuclear weaponry. Bomb and kill any high ranking, or even mid ranking military leaders every chance I got and of course all high ranking civilian leaders. Bomb and destroy all heavy military equipment including tanks and plans. Destroy any artillery and missile emplacements so they can't shot at you. That would probably be first. Finally, bomb any large troop formations and do that while an allied force like troops like those from South Korea move in on them.
Of course all human shields that the forces against you use would have to be completely ignored. If anybody tires to use a guerrilla campaign against us I would even mess around and give them a chance to do it (plus the troops are not going to stay there for them to engage anyhow), after all in that scenario we’re not preserving anything or nation building. I would just surround the cities or places where those people are, give all non-combatants a day or so to evacuate unarmed, because if they are armed they get shot on sight, and destroy wherever they are by razing it until it doesn't exist anymore. There would be no troop presence to keep the peace or anything like that because they are just there to destroy our opposition, not help them rebuild. Even if they have nuclear weapons they don't have a lot of them at this moment and don't have good delivery systems with them. That might be a good reason if we are bound to have a conflict we do it now instead of waiting for them to have a good stockpile. In the even they use one that just gives us a legitimate reason to use or own and utterly destroy everything, like area saturating every important place over there with our own.
When your vastly more militarily advanced and capable than the opposition there is no way they can beat you unless you do like I said and try to nation build, try to take over the place, or try to have a presence there.
Part of the benefits of doing something like that to North Korea is that the people are so impoverished and their quality of life is so bad that even destroying most of the infrastructure doesn't really hurt them that much or chance that much for them. In fact it might allow people that really care to actually get food to them instead of food aid being funneled off to support North Korea's army.
Of course it's bad for the truly innocent civilians caught in the crossfire, but then again you can blame their government for that, and the fact they have did nothing to resist or overthrow them while living under a brutal totalitarian regime.