Assuming an invasion of SK-US joint operation, and with the knowledge or at least very credible assumption that NK has nuclear weapons,
Situation 1: NK launches nuclear warheads using missiles.
Result: Mobile missile defense, which would be deployed using the above assumption, would neutralize the missiles. It is unlikely this system would be overwhelmed as the NK likely does not have enough missiles or nuclear warheads.
Anti missile weaponry isn't perfect. Even the best systems only have a 75%-80% success rate* for intercepting missile weaponry. After all, a ballistic weapon is pretty stealthy, once the burn stage has been completed.
*Don't ask me where I got this number, can't quite remember
Wish you could remember though. I'm wondering if that does apply to ballistic weaponry or not, what era of missile defense it is (because I'm absolutely positive we have stuff now in that category that the public is unaware of), etc.
You're also forgetting the chance for Nuclear suicide bombing. Place a nuke in a submarine, float it under the closest US fleet (Sub will go undetected as it can stay deep in the water, and doesn't need to open hatches to fire it's torpedo's, for example) and detonate. A few weapons detonated in such fashion can eliminate concentrated US fleet presence in the near Pacific.
I would be very, very, very, very surprised if the NK had any submarine that did not sound like a barn full of farm animals being set on fire on sonar, and considering everyone tries to keep tabs on everyone else's subs, even in today's age, we'll likely have sonar listening posts nearby (esp. due to Russia's proximity. Cold War-era sonar stations, even if they haven't been upgraded since, should still identify anything the NK has).
Still, suicide bombing is a valid option, since
You can replace the same scenario with a pick-up truck and Seoul.
is definitely possible, too.