[1] Kill the
NPT. There was already a distinct trend toward proliferation.
[2] Then have the
MLF go ahead, so more NATO states have access to nuclear weapons technology, and widened to handle land-based tactical weapons with a common stockpile.
Switzerland, Sweden and Italy had a cooperative agreement to share development of nuclear weapons, support technologies and delivery platforms. That'll bring in Yugoslavia (and perhaps increase the status of a "Third Way" or NANA block who'll want nukes).
Without US pressure Taiwan and South Korea will join.
Israel is inevitable, without significant historical changes.
[3] Have the UK spread the costs to other Commonwealth states, so Australia and Canada also build their own weapons (possibly with US assistance depending on the relative strengths of the relationships).
Indonesia had a nuclear energy programme in the fifties, this could extend into weapons development. Especially if Australia has them.
India and Pakistan are also inevitable.
Iran under Pahlavi was interested, especially in electricity production. They were expected (OTL) to have nuclear weapons in the 1980s under the Shah. This will probably pressure other states in the region.
South Africa may progress faster given involvement in a Commonwealth programme.
Spain under Franco will be very interested, especially given the French and Italian programmes.
Germany and Japan will easily develop the capacity but will face opposition. However the greater proliferation will weaken this so inevitably they'll also develop nuclear weapons.
Egypt was interested and, with assistance, could join the club.
In South America the ABC powers will also develop nuclear weapons, Brazil first.
So that's 26. More after the USSR fragments.