And is China a credible global nuclear threat? China's global economic domination makes nuclear war both unlikely, unnecessary and economically suicidal.*
At the moment, though they are on a reasonable trajectory at the moment, that could easily change. Ignore the possibility at your peril.
China-US confrontation however is a different matter and should not be an element in British deterrent policy.
Should and doesn't can be to different things. When dealing with things on these scales there are no real borders apart from political, and the world is small. The enemys will try and wedge you and your partners, relying on the weak within you to go, not our problem.
History is a merry go round.