I can only guess but nuking a few warships out in the ocean, away from population centers, will not be viewed with as much revulsion-condemnation as using a nuke on land forces. Nuking the ships will kill only combatants, there will be no collateral damage
It won't matter. It'll have the same galvanizing effect Pearl Harbor did. A backward country like NK is suddenly going to have dispatched a nuke.
The pressure to destroy NK would be immense, collateral damage notwithstanding.