i dont think they had the weapons, just the knowledge and research to make them.
not sure on that.
There were Soviet nuclear missiles located in Ukrainian SSR.
Due to the chaos during the break up, of course USSR didn't have possibility to evacuate all the weapons systems from now-independent republics.
Among the nukes located in Ukrainian SSR were R-36 "Satans" (10 warhead monsters). There was more nukes based there than what Britain, France and China had combined.
As well there were dozen or so (can't remember exactly) of heavy strategic bombers (meant to carry nukes) located in Ukraina. Russia bought some of them and the rest were scrapped (A shame but Ukraine didn't want to give them free and Russia at the time was basically bankrupt too).
As said, all the nukes were dismantled under international agreements starting from 1994. Russian Federation, USA and UK agreed to ensure the safety of independent Ukraine in case Ukraine was threatened by nuclear strikes.
I think the agreement was not ratified by too many countries after all. It was a top priority for international community to prevent former Soviet nuclear arsenal ending up in wrong hands.
"Satan" missile in museum in Ukraine:
Tupolev bomber being scrapped in Ukraine: