You said "I assume much more countries secretly have nukes".
I claim that beyond the open secret that is Israel, the number of countries controlling a right-now detonatable nuclear weapon who are not on the Wikipedia list of "countries with nukes" is less than 5.
Claiming much more countries secretly have one, is not at all the same as claiming most countries secretly have them. And I agree that it won't be many many, but in this context one previously unknown bomb already might change lots of geopolitical equations and their outcome.
I claim that beyond the open secret that is Israel, the number of countries controlling a right-now detonatable nuclear weapon who are not on the Wikipedia list of "countries with nukes" is less than 5.