Ukraine proved you should keep them.
1. The worry of invasion
2. The worry of implosion
South Africa in the 1990s was at a very risk of imploding into civil war. Access to nuclear weapons would have made this risk of implosion even worse.
This was a similar worry most of the world had about Ukraine and Kazakhstan after the USSR collapsed - look at what happened to Tajikistan, Georgia, Moldova, Armenia, and Azerbaijan in the 1990s. Hell, there was even an attempted coup in Moscow in the 1990s.
The fewer countries that have nuclear weapons, the easier it is to decrease the chances of the next conflict (war or civil war) using nuclear weapons.
And I would posit that the aim of limiting countries with nuclear weapons is simplistic. If a nuclear power decides to terrorize a non-nuclear, but industrially advanced neighbor, the victim is likely to acquire a nuclear capability, one way or another, either now or in the future. It hasn't happened yet with Ukraine, but I believe it is inevitable.
Furthermore, that nuclear capability will come with a (justified) grudge. I would certainly want to vaporize my bully.
The end result is that the probability of nuclear conflict has increased, not decreased.
A major worry at the time was that individuals in Ukraine could sell those weapons and the know how to the highest bidders.
It wasn't an unlikely prospect - China, Pakistan, and India all bought defense IP from individuals in Ukraine during the collapse of the USSR and before post-Soviet states governance were formalized (eg. China and India can now manufacture Aircraft carriers, nuclear submarines, and turbofan jet engines because of IP they bought using questionable methods in Ukraine in the 1990s)
China's Jet Turbine Program - https://www.airuniversity.af.edu/Portals/10/CASI/documents/R...
As well as this co-investigation by the SIPRI and Reuters [0] into Ukrainian defense IP sales to China.
What are the "accusations" of mine that you would call wild? I can give citations for all that are needed. I just sometimes don't on HN because citations take time.
[0] - https://www.reuters.com/world/china/ukraine-crisis-threatens...
Ukraine had huge arms and aerospace industry. They would have capacity to replace detonator units. See [0][1][3], they designed and built quite a lot of ICBMs. Saying they would not have control over missiles they designed and manufactured does not make sense.
[0] https://en.wikipedia.org/wiki/Khartron