North-Korea has attacked South-Korea

Very true. Remember also the fact that North Korea also has limited logistics as well like food, water, etc. since their famine recently. The same thing happened during Desert Storm with Saddam Husein's army as well. In fact many of them surrendered out of just wanting food or water due to their poor supplies. Plus take into account that many of these people might also only be armed civilians forced into service who would quickly run away, surrender, or shoot their own leaders just to taste freedom.

If anything you'd see more people surrendering just to get humane and ethical treatment, food, water, medical care, etc. In short, if they did try anything, North Korea would have the advantage for the first few days, but when food becomes scarce, water goes bad, supplies run out, people get tired of being in a war they didn't want to fight, what would become the Greatest Conflict of the Korean Peninsula of the 21st century would collapse into the Greatest Humanitarian Disaster of the 21st century.

So if anything any action taken by the North against the South would only inch them further into decimation, destruction, and total collapse. If the North wants to survive the best thing they can do, is actually sit back and do nothing.

Thing is the soon-to-be new leader's gotta demonstrate his ability to rule somehow. That's what this whole offensive thing's about IMO.

And these people have been conditioned to fear their superiors and obey their rulers, they won't easily want to surrender unless their generals do, and given the totalitarian nature of the Kims, I doubt that will happen within a matter of days, or at all even; they might fight to the death.