Russia and China are not going to give up nukes any time soon. If the US under a future president decided to try and negotiate disarmament to eliminate all nukes then that might work. I think that's the only way Russia or China would give up nukes. Until then I think Europe should keep nukes as a deterrent.

So yes, multilateral disarmament could work, and could prevent lots more countries from building nukes. I don't think unilateral disarmament is a good idea though.