That is highly unrealistic.
Any US attack on NK nukes will the same as if the US started attacking Chinese or Russian nukes, or vice Verda, and present Fatty K with the classic 'use them or loose them' dilemma.
There is absolutely no way anyone could convince Fatty K that after the US has destroyed all his nukes that the next step won't be regime change or an US nuclear first strike.
As such, he will most likely nuke Seoul and every other major target his nukes can reach out of some desperate hope that such a move would force the US to reconsider or just out of sheer spite.
Even if Fatty K holds back or cannot launch any nukes, NK 'rocketing' SK in response to such an attack won't just be a few random shots for show, but a full sustain barrage from tens of thousands of heavy artillery and rockets aimed at Seoul.
Most of those artillery pieces and well dug into mountains, and it won't be quick or easy to silence them with air strikes alone.
Indeed, the only way to totally silence them will probably require boost on the ground to dig them out. And the pressure to act will be irresistible for SK with millions of civilians trapped under bombardment in its capital.
Once SK and the US gets sucked into a ground war, it will be virtually impossible for them to pull out half way, because Fatty K will do all he can to force them to advance ever northward since his only hope in such a situation would be to force China to come in against the US and SK forces.
Basically, as soon as the US targets any NK nukes, the domino effect to the re-start of the Korean War will be near impossible.
I hear what you saying, but I disagree, IF US actually bombed NK nuke sites and destroy NK nuclear capability, they would not go ahead and invade or do regime change simply because China won't allow it and from this fact alone it will not happen.
Also in reverse if US is not going to do regime change and just destroyed NK nuclear sites, then NK won't attack SK or US because it know its suicide for them, as you said, they might kill up to a few million in the first few days with artillery strikes but there is no outcome that NK military would win in a full scale war against SK.
But since I don't think any type of strike will happen so its a moot point, but just in case if US attacks NK nuclear sites, they would probably get secret ok from China, but China would also give US the red line that it cannot cross.