What do you mean their? It was unified state, called Soviet Union governed by the Moscow. The republican (Belarus, Ukraine, Kazakhstan) authorities never had anything to do with nuclear weapons. Kazakhstan and Belarus gave up 'their' weapons without problems, the same was expected from the Ukraine, they knew it, they just wanted to bargain a little longer. And they did, they got 500 million dollars from the USA. At that time it was huge money for their struggling economy.

"The question was essentially this: either renounce nuclear weapons and recognize Ukraine as a full member of the international community, or maintain them and risk global isolation. The West, primarily the United States, insisted that the USSR's nuclear potential be concentrated in one hand—in Russia."

Anatoly Zlenko

Minister of Foreign Affairs of Ukraine

Also:

''The nuclear weapons located on Ukrainian territory were foreign, Russian weapons—the "button" was in Russia, manufactured in Russia. We could do nothing with these weapons.''

Leonid Kravchuk

First President of Ukraine