Why do people keep parroting this false trope?
They had no other choice but to hand over their nukes since the nukes were never theirs to begin with, they belonged to Russia, and they had no launch codes for them anyway, which were in Moscow, nor the resources to maintain them.
And that's not exactly what the world needed at the time: unkempt nukes in the hands of a bankrupt and corrupt nation going through political and economic turmoil of the 90s USSR collapse, guaranteeing them to get "lost" and end up in the hands of despots and warlords.
So giving them up was the correct and only choice for them. Otherwise they would have been persuaded by force to give them up either through sanctions or even through military intervention.