First, China has absolutely no interest in overthrowing N. Korea. N. Korea is a useful pawn serving their interests and a buffer against incursions from the West. Your casualty estimates are also terribly low given that Seoul, Incheon and a number of other large S. Korean cities are well within the range of rocket and artillery fire.  N. Korea also has extensive tunnels and other preparations for all out war all across N. Korea so it will be hard to find mobile nuclear launch platforms. That means the successful launch of nuclear weapons and chemical weapons is inevitable.  Your estimates, in terms of casualties, therefore, should be more in the range of millions, not thousands. It would only be a Pyrrhic victory in the best of outcomes.