Japan may not officially have nuclear weapons, but they do not lack the capability - if they decided to weaponize (which would never happen short of a Chinese existential threat), they could do so in a matters of days, not months - the nuclear knowhow is clearly there.

The rest of your point is fair - for Japan to go to war would take a fundamental shift in the country, and its questionable whether the Senkaku Islands would meet that level. China is an aggressive, scary power in a lot of ways, and we ought to be cognizant of the dangers it poses - and the Japanese (and the Vietnamese, and the Phillipinos) are.