So on the question, in my opinion, if anybody does not have the “right” to own nuclear weapons, then neither do any of the regimes that have them.
Me being a sort of anarcho-capitalist, theory says anybody has the “right” to own anything they acquire either through honest non-coercive trade and/or “homesteading”, which means taking possession of unclaimed resources and using them.
BUT they would NOT have the right to use them in any way that would violate the “principle of non-aggression”. That would also prohibit the threat of the use of them to exact some behavior from another, for that would be an aggression. It seems that the implicit threat also falls under this rule, but only if an objective threat, not a subjective threat.
Of course that would mean that almost nobody at all could use them, except as a defense against threats to use them, I suppose, but in the kind of world where everyone understands that only “legitimate” political philosophy is based in non-aggression, anyone who owned them would lose a lot more than the value he could get from them, for nobody would really want to do business with them.
But the citizen has a right to defend himself, and join with others to that end, when freedom is threatened by a government that spies on everybody, orders hits on anybody it considers a threat to its rule, and is engaged in a series of increasing attacks on the freedoms of speech, press, religion, assembly, the right to “be secure” in their person, papers, effects, and property from government confiscation, the right to trial by jury, and to a state government with a “republican form of government” (Article IV Section 4), which also means free of interference from the federal government in state matters, of course.