I suppose that if this is within the 20 year limit, the question would be limited to Israel, post-Soviet states within the first 4 years of existence, South Africa's early program, and US/Russian/Western European actions in the early 90s. While Israel and S. Africa's programs were developed during the Cold War, I'd like to concentrate on regional uses/threats.
Also, I guess I'm disqualifying US threats against Japan during WWII, as I'm primarily interested in a context with the risk of nuclear retaliation.
Let me try to break this down:
Israel
Yes. Israel has used the threat of nuclear weapons reportedly, but they have an official policy of nuclear ambiguity, so there's no confirmed proof. But we're pretty sure they're used it. I'm fairly sure that it was threatened in the Yom Kippur war under the name of the "Samson Option" (1973 War, widely seen as revenge for the Six Day War of 1967):
In Israel's case, the doctrine of nuclear ambiguity is embodied in the "Samson option"-namely, the use of nuclear weapons only as weapons of last resort. Adherents of this policy argue that Israeli nuclear ambiguity not only fosters deterrence but also allows the government to minimize the adverse political, military, and diplo- matic ramifications of Israel's regional nuclear monopoly.^^1
It is widely said that Israel used this threat in 1973, threatening "very serious conclusions"^^2 (and placing forces on nuclear alert), to force the United States to airlift supplies. The United States complied.
Now, Israel isn't the only one who does it. Obviously, we all know North Korea does it, but the US's protection of South Korea and the lack of a reason for it rationally being done (if North Korea nukes South Korea, they will be nuked by the US, and no one will protect them, and they can't retaliate against the US with their current tech...so they're helpless), means they're not as seriously considered.
Similar to Cold War tactics (though a little more blatantly outspoken, I suppose, in some cases), India and Pakistan have also threatened each other with nuclear war. Last article I saw on it cited India saying it would retaliate with nukes if attacked by nukes, and Pakistan does pretty much the same thing. They are both boasting, bigging themselves up, in the hopes of deterring each other and trying to get their policy goals (ie. no disputes over Kashmir, etc.).
I don't know much about other nations, and Israel is my particular specialty, but the short answer is yes; nuclear threats have happened outside of the Cold War, and are used regionally as well.
^^1 The Mixed Blessing of Israel's Nuclear Policy Zeev Maoz International Security , Vol. 28, No. 2 (Fall, 2003) , pp. 44-77
^^2 Hersh, Seymour (1991), The Samson Option: Israel's Nuclear Arsenal and American Foreign Policy, Random House. (Disclaimer: I do not own this book, I've just seen it cited in numerous political science/history papers, it is them I am referencing).
You should definitely add India/Pakistan to your list. They are both nuclear powers that actually have been in active conflict after the end of the Cold War.
Israel has never acknowledged that they have nuclear weapons, and South Africa never acknowledged them until it dismantled them, so neither could have ever used them in this fashion.