China doesn't likely want a proxy war. There is no real reason to think China would want North Korea to ever attack the South or do anything else other than occupy space. China doesn't want a unified Korea because it would become an even bigger economic power which is friendly to the United States and right on their border. If the North attacks, they would lose fairly quickly and the peninsula would be unified in a way that China has been trying to avoid.
You also significantly overestimate North Korea's military power. North Korea's economy is a tiny fraction of what South Korea's is, and they don't have much modern equipment. North Korea's military is largely comprised of antiquated junk. South Korea has a first world military. Sure the North has lots of hardware, but in reality it is so over matched that the South would win in not very long. North Korea would be wiped out of the skies within a day or two and then their army would be easy pickings.
If North Korea attacks, even with poison gas lobbed at the South's airfields, they couldn't sustain an offensive for long. They'd lose control of the air almost immediately and once their initial burst was absorbed, they'd simply be wiped out. They could kill a lot of civilians in the first 24 hours with artillery, but that wouldn't help them win a war.
Yeah verily! And China does not want another Democracy on it’s border.