First, China has to make sure the US is busy somewhere else. Who knows, they might trigger a US V NK war to get the US assets committed away from Taiwan.
That is a guaranteed way to loose one of their last major allies. Because I can guarantee that if North Korea was stupid enough to attack again, the US and other allies this time would not stop until the entire peninsula was reunified under South Korean rule.
That would harm China, as both a unified Korea would be serious competition in global trade, as well as it would remove their main "attack dog" when it comes to international exposure. For the last decade or so, China has been presenting itself as the "one nation that can keep North Korea in check". If North Korea was to start another war, all of that would evaporate.
And expect a lot of other nations jump into that conflict also.
Japan only recognizes South Korea as the "legitimate government", so I have no doubt if asked they would join South Korea.
The Philippines participated in the Korean War, and have been trying to bring the nations even closer. So expect them to join in.
The UK have been important strategic partners since the country was founded, and frequently conducts military exercises together, so they also would likely jump in.
The EU is the largest trading partner of South Korea, both import and export. 45% of EU foreign trade goes to South Korea. So expect a great many of the EU nations to join in (including France, Greece, and Germany).
No, reigniting the Korean War would be the last thing China would want. That would guarantee a great many nations would then have a military presence in the area, which might otherwise sit out a "China-Taiwan War". And without China to intervene in a new Korean Conflict and a much larger US military presence in terms of ability to respond, that conflict would be very short.
It must be remembered that North Korea attacked last time in July 1950, pushing South Korean and US forces all the way to the tip of the peninsula at Pusan. And 2 months later (September) they broke out and ran all over North Korean forces, a month later (October) ending all the way up at the Chinese border. This time they would not make the mistake of inviting in a Chinese Intervention, probably stating their intent to stop say 25 miles from the border and allowing no ground forces to move north farther than that (and probably no air forces closer than 10 miles).
And it took the North Korean - Chinese forces 2 months to battle back to the original border. Seoul was attacked again, and after a 2 year stalemate the UN forces were once again pushing hard back into North Korea when the armistice was called. That is why the border still rests North of the original one. China had already "shot it's wad", and the North was in danger of being rolled up all over again.
Next time, it is guaranteed that the offensive will not stop until the entire country is unified. And with the actions of the last 60+ years, do not expect much support for this from the North Korean population. And after reunification? Well, expect at least 1-3 new US bases on the Peninsula. I would expect 2, likely a joint Army-Air Force one, and the other a Navy Base with a large Marine contingent. Yonpo Army Airfield and Wonsan Naval Base are likely candidates for permanent South Korean - US bases.
That would be the absolutely last thing that China would want to see.