Japan, Taiwan, and South Korea have excellent engineers and physicists. They also have much fissile fuel from the nuclear reactors used for electrical production. They would be fools not to deploy nuclear bombs in their arsenal of defense against China. They might also ask Israel for their nuclear weapon designs most politely as we all know they work. Israel knows they work but have never tested their designs. Why test our designs that have been tested and do work.
They could not defeat China in a nuclear war. They could make the cost of war to high for China to risk it.
Oddly in a nuclear exchange China would defeat Japan, Korea, and Tawain would be a loss as cental control of the communist party in Bejing would no longer exist. China would break up.
Hard to imagine any of those three countries doing so. Japan...mainly because of history. Taiwan...because they'd fear immediate invasion if Beijing ever got wind of the program. South Korea...ditto if Kim Jong Un ever got wind of the program.