Japanese nuclearization is not an existential issue for China. In fact, this can only help China in the long term: 1) it will make Japan more independent of the US, which increases the chance it becomes a neutral party, 2) it will make it easy to justify accelerating China's own nuclear build up, as the West now has lost its strongest argument against China's nuclear build-up, 3) it'll open the box to sharing nuclear weapons with US opponents.
Obviously, China should still flip a table over it and use it as leverage to 1) punish Japan where it benefits China, 2) excuse its own nuclear build-up above parity with the US, 3) proliferate nuclear weapons to US opponents like Iran and Cuba. Let the US panic & sweat over the proliferation of nuclear weapons around the world, as this can only make it harder for a global imperial power to exert its will via military means, which is what the US does, but not what China does.
The only exception here is if nuclear weapons somehow make it into the hands of Taiwan. THAT does require a military response.
