That isn't too surprising, but the South doesn't want to. I mean, it'd be like German reunification on Hard, nay, Insane mode (Kim Jong Un mode). It's East Germany's problems multiplied, economic, social, etc. Minute the government collapses (and, crucially, Chinese funding is cut off) North Korea is Somalia with snow and a secular militia in charge instead. The sheer social, economic, political changes required boggles the mind. I want them together as much as you do, but I can see why the South (and China, for many of the same reasons) is reluctant.
I have never seen anything to show that "the South" is reluctant to unify, rather, unification is something of a priority. I've seen Southern people saying that they're concerned that it'll really damage the Southern economy, but the governments remain very much in favour of unification and that would be the word on people's lips if all hell breaks loose. This is just something the South has to stomach though, it'll be painful and it will rock the economy but it just has to happen.
If China wanted to, they could go Putin and simply annex the whole fucking place, and not a damn thing could be done (the US certainly isn't going to start WWIII over it).
China annexing a part of Korea (that's what we're talking about here) would be the deathknell for all successful Chinese foreign policy. Ever. If they did that they really wouldn't give a damn about anybody else and could comfortably become a pariah, when in fact the entire Chinese economy depends on people buying their stuff. Being a pariah and subject to sanctions is unwise if your economy is set up like that.
If China wanted to, they could set it up under some other, more Chinese-like dictator, and modernize it as a vassal state that would be grateful to their new (old really) Chinese overlords.
This is more likely but the moment the word "unification" starts popping up, no Chinese-like dictator will be able to stop that tidal wave. You've seen the Arab Spring, you know what happens when things get into full swing, not like in Bahrain or Algeria but when people really rise up they can't be stopped without massive bloodshed.
If China wanted to, they could kill half the population within months simply by not doing anything and watching the fireworks.
If China did this the finger would be pointing squarely at China and we're right back to option one. The Chinese would be internationally reviled for allowing this to happen.
If China wanted to, they could simply send the Un to the UN (and probably the Hague) and give the North to the South over the threshold.
This is the most likely course of action I think, and the most sensible if China wants to rehabilitate itself within the international community.
If China wanted to, they could force the North into an suicidal attack against the South, and America if it is in reach, and kill millions.
This is a ridiculous option that would be even worse than just sitting back. If they force any kind of attack then yes it would be WW3, or whatever the step below that is. Cold war perhaps.
China holds most of the cards here, the only question remains what they want, and what they are willing to stomach; both to their own population and to the international arena. China doesn't want millions of impoverished Koreans opening up it's doors, and it is trying to figure out how to get rid of them. But don't think that if they sincerely wanted to keep the North in their pocket forever, they couldn't do so: they could, they just realize they'd have to invest more then they are willing to, which currently isn't much.
China holds most of the cards but they have few realistic options. They can choose to support the Northern government until it becomes completely untenable, in which case they sort the situation out themselves (invasion) and reform the government/install a puppet as we've discussed, or just bite the bullet and give the North to the South. If they sincerely wanted to keep the North in their pocket forever they'd be completely delusional because the North is existing on borrowed time. We're talking about a government that will blow their own generals up with mortars in public executions to make examples of them - trying to reform that mess is an exercise in futility.
Remember, Putin's annexation policy only worked in Chechnya because nobody really cared about the Chechens except Gamsakhurdian Georgia and Estonia. And John McCain. They're just Muslims anyway (who cares about those weirdos and their beards and gold teeth) from a country nobody's heard of, plus they were often Islamists and terrorists and anything is better than Islamic extremism, right? Even totalitarian, dictatorial, corrupt puppet-regimes with institutionalised brutal torture, disappearances, execution, sexual abuse and religious dogma. I'm sure. Those "monkeys" couldn't run their own country anyway, they're too crazy. I mean, it's not like they're human beings, right? North Korea on the other hand is not Chechnya, it is half of an ancient nation known to practically everyone and is very much in the public eye. Annexation would simply not be possible. Even the supposedly ambivalent South would be in uproar over that one. No Southern government would agree to half of their nation being annexed by anyone.