Argentina will want them, if Brazil hase them.
The Treaty of Tlatelolco would not exist ITTL.
There would be considerable pressure on Germany and Japan not to do THAT, as in, please, really don't. We mean, seriously. That would be especially badly regarded for Japan, including by a vast number of Japanese.
In particular, if this is in a Cold War context, IF West Germany does it, East Germany will want to do it as well (and vice versa), which would make the screams of horror and disgust from both the NATO and the Warsaw pact audible from Alpha Centauri.
It's hard to see why, however. Everything under the NATO and Warsaw Pact nuclear umbrellas would have little point in doing that, except for particular contexts (see for Turkey below) or as display of power ad autonomy (Britain and France IOTL). Display of power and autonomy from German quarters during the Cold War is NO, JUST NO.
People would be floating Morgenthau plans around as soon as either Germany begins suspicious enriching, I'd suppose.
In a proliferation context, Francoist Spain could be interested, though it may lack the capability/money. So could Turkey in the seventies/eighties, especially if other ME countries like Iran, Iraq or Syria are running significant and dangerous-looking nuclear programs.
Asia might be nasty. Vietnam, Indonesia, possibly Burma, both Koreas, Taiwan... at which point Australia gets nervous and decides she need her own deterrent, you know, just in case.
Add a regional nuke arms race in the Middle East, and at least attempts at it in Africa if Apartheid SA keeps both the damn things and, by some miracle, Apartheid.
Hmmm.
A worrying world.