While the song blasting retaliation may make for a funny story, North Korea is no laughing matter. They are dangerously opaque: we are not even really sure what powerful weapons the North Koreans might have because their security is so high and their borders are closed. The sinking of a warship is a serious military action and South Korea should treat it as such.
North Korea has left its people to starve and suffer for years. The situation isn't getting any better. It would be painful to go in and correct, but it is time. There is ultimately more good to come from taking out the North Korean government than there is from continuing to allow all of those people to suffer.
South Korea can blast kpop and propaganda, but not make it seem like the country is panicking or threatened by North Korea. Basically it's like they're going "yeah, whatever" to North Korea, and not escalating the response, but at the same time, letting NK know they're not scared. I'd guess if there's a need to respond with military action, SK can do so, but this way, so far no one's getting hurt.
A forceful military response does not always fix the problem. More often than not it makes the problem worse. What Korea needs to do is get over it's bullshit and mend relations with itself instead of putting up walls and borders. We are getting nowhere with these conflicts and we need to try smoking the proverbial peace pipe.