Ukraine never owned any nuclear weapons, only hosted them on their territory. Russia inherited all the nuclear weapons in the former Soviets when the breakup took place. This is legally codified in the founding documents of all the former Soviet territories...including Ukraine.
Ukraine never controlled the nuclear weapons on their territory either, they didn't have the nuclear launch codes and didn't have the technical expertise to maintain them independently. The only value to Ukraine would have been to sell the warheads to the highest bidder, which Russia and the other Great Powers wanted to prevent.
The Budapest Memorandum was a diplomatic fig leaf designed in part to prevent Russia from using 'other means' to safe guard the weapons. Both sides have violated its terms by meddling in Ukraine's domestic affairs since then.
The nuclear codes weren’t technically connected to the nuclear weapons - they didn’t “unlock” anything. They were just an authenticator sent to the officers in charge of the control station. Only the US implemented a remote-unlock system for some weapons, toward the end of the Cold War.
“Technical expertise” needed would have been minimal. All of these weapons could have been dismantled and the nuclear material (plutonium) removed at the very least. That is the main requirement for building a simple nuke. And there probably were Ukrainians who could have maintained much of the weapons materiel left in Ukraine at the time.