Realistically the only enemy Franco's Spain would have is the USSR/WP. While the French have gone with their own Force de Frappe the reality is that absent the US/NATO umbrella, still in place even though France is not in the command structure, this basically amounts to a "we can hurt you badly while you totally destroy us" response. Getting the US umbrella and being in NATO with Article Five is a much better nuclear security blanket.
Wait, is? The USSR wasn't going to nuke Spain without a WW3, and in a nuclear WW3, the few dozen bombs Spain might deliver to the USSR won't make much of a difference compared with the thousands the USA would throw at them.
So, as an independent deterrent, the UK can tell the USSR: if the nuclear genie remains in the bottle, but you happen to be able to invade us anyway, we will nuke you. So don't. France can say: If you get West Germany without nukes, don't cross the border, or we will nuke you. So don't. Spain? It's "If you got there, France already nuked you, you've nuked them and the USA nuked you, so what difference does it make". I mean, even if the USA wouldn't nuke the USSR during an invasion of France, France would threaten that, and that means Spain is protected, NATO or not, at least by France's Force de Frappe.
And, in NATO, Spain becomes part of WW3 and a nuclear target. Outside NATO, Spain can tell the USSR "We aren't getting involved, in return, don't nuke us". The only domestic nuclear deterrence which would make a difference, I think, would be outside NATO, and it's "Hi Moscow, we've just noticed WW3 has started. We aren't getting involved, so don't nuke us or we will nuke you".