First of all, if you "...depend on South Korea and China for up to 80% of its trade and 35% of its GDP." why would you sink one of it's warships?
Becuase Communism fails every time it is tried and the only way to keep the people down is to lie about the rest of the world, and, to create enemies for those same subjugated people to hate. Now the North can point to the trade embargo as the reason it's people are starving, not the failed policies of left wing politics.
Rather than en embargo, South Korea should begin to airlft food to the North. Free food would hurt the government of the North more than taking food away. Along with the food could come pictures of free people.
Just a thought, attack the North with love, butter not guns, and in this case it might work.