"I just heard this morning on the radio that Japan also wants to have the nuclear weapon. Being its sole victim, so far, it's quite a news!"

Politically it seems pretty unlikely, but with N Korea continued effort to have nuclear weapons, this is enough of a wild card, that it could change this political reality. I would predict that if Japan does go nuclear, they won't want to have a few nukes, but will want to have quantities of nukes at least equal to France's arsenal, though not as much as the US [no country rationally needs this many nukes].
If Japan goes nuclear, that also probably means they are also going to want to test a few of them- this fact would push the US to the position, of wanting to give our nukes and our technology to Japan- thereby removing any need for Japan to do these tests.
Of course, with Japan it's not a question of whether they have the technological or economical capablity- but rather it's a question of willingness to go down that political path.