This is only my opinion.
In a conventional war N.K. will collapse like a house of cards.
Their armed forces have low morale and the population at large has little genuine(as opposed to feigned) loyalty to the present regime).
Most of the work would be done by allied airpower with ground forces mopping up.
Their nuclear assets would be taken out almost immediately probably by conventially armed cruise missiles, special forces (most likely Delta) or a combination of the two.
The U.S. would not use nuclear first strike under any circumstances, there is even the possibility that they wouldn’t retaliate in kind if N.K.initiated a nuclear strike; but I wouldn’t hold my breath on that one.
There wouldn’t be any post conflict insurgency as I believe that the Koreans ethnicly are a homogenous group unlike say the Iraqis who have various divisions both on the ethnic and religious fronts.
(I may well be making an incorrect assumption here so feel free to correct me if I’m wrong)
Plus they would nationally be reunited with S.Korea in much the same way as the Germanys were reunited.
The big stumbling block is China.
China knows that Kim is a total nut job but they wouldn’t like having the U.S. active in what they consider to be their sphere of interest.
Its not so much about actual power as it is about imperial pride.
As an example look at how Russia views former Soviet republics even though for the most part they hold a strong antipathy to Russia.
Perhaps a deal could be worked out if S.K. in advance made some economic and political treaties with China bringing them closer together, possibly involving the downsizing of Koreas armed forces and the Americans removing their own armed forces from Korea.
But I really think that China would intervine or threaten to.
Of course they might send forces to beef up N.K. and then absorb N.K. in to being a defacto part of China.
All of this is only my own kite flying though.