Regardless of the tendency for modern day liberation movement politicians who use camoflage garb and weapon symbolism to portray their activities as some kind of successful military struggle, it was the international bondholders and the domestic protest movements that actually made a difference.
At no point in time was the Apartheid government in military danger of having its frontiers breached, nor was it in any danger of falling to internal rebellion. The most violent part of pre-democratic South Africa was the modern day KwaZulu Natal province, where the UDF and later the ANC and the Inkatha movement fought what was essentially a paramilitary blood feud, and had the Apartheid government actually cared about that part of the country (they didn't, for reasons of racial demographics), the violence could have been substantially clamped down upon. But they were never going to nuke it.
The Apartheid government had two big problems: 1, they couldn't militarily engage the biggest danger to the state, which were international sanctions and the UDF, and 2, the writing on the wall after the Rubicon speech made corruption in the civil service radically transform from a relative non-issue to a massive one almost overnight, as it became clear that there was a limited time to loot and everyone wanted in.
None of these issues could have been solved by a nuclear bomb detonation.
Now, if a military coup by hardliners happens, things change drastically. The issue of civil unrest gets way worse and bloodshed from it would as well. Conscription resistance would actually be a problem; SADF discipline & morale in OTL was actually pretty good, despite political fractures in the white community stemming from the English/Afrikaner split; it would be much harder to paper over in this case. There would probably be multiple Marikana type incidents in labor disputes. The state would go from being a pariah to being an utter leper. And the nuclear program might, if the coup elements are extreme enough, be considered as something to start flaunting. Do I think they'd nuke Lusaka, Harare, or Luanda? Probably not. But international mediation would be much harder to bring about.