And then watch as the North Koreans launch nuclear/conventional missiles against U.S. bases in South Korea and Japan?
Well I was imagining that South Korean forces would do it, considering South Korea was attacked in what it recognizes as South Korean waters, only South Koreans died, and the South Korean armed forces are now in the lead role in the defense of their own nation.
While we have to imagine nuclear retaliation as a possibility, it is quite unlikely considering it would result in the certain elimination of North Korea and the Kim regime. The Kim regime's main priority is it's own survival, so, if South Korea takes limited, eye-for-an-eye military retaliation and kills some North Korean sailors, Kim is faced with a choice. As I see it he has 3 options. He can A) Hoot and holler, and call South Korea and America all sorts of names, possibly withdraw from talks, and play it up in internal propaganda B) Escalate with some form of conventional military action, or C) do what you suggested and fire nuclear weapons.
Now of those options, option A is the most likely to assure the continued survival of the Kim regime. Option B is less likely because it leaves open a path to war which will destroy the Kim regime. Option C ensures the Kim regime's destruction. So since we more or less know that North Korea's #1 strategic imperative is to maintain the status quo, we can be reasonably certain that it will pick option A. It enables them to play the victim and spread propaganda without actually threatening survival.
Furthermore, South Korea has sunk North Korean ships before and killed over 100 NK sailors in sea border clashes since 2000 and North Korea never got too crazy over those. There have been much larger land border infiltrations by North Korea that did not lead to full scale war, so I see no reason why limited retaliation should.
Lastly, I think military retaliation would show North Korea that getting the bomb has not left it invulnerable to punishment. If South Korea does not retaliate, they risk allowing the North to think that nukes are an invincible shield behind which they can provoke endlessly without any consequences. If the South disabused Kim (or whoever is in charge in Pyongyang) of that notion, then it might actually make disarmament more likely, because the North will realize it's nukes aren't worth as much as it thought.