If you are travelling HBO then 1:45 hrs should be enough time to get through immigration and re-clear security for your domestic sector. My understanding is with checked luggage you would need to collect in JNB and pass through customs before re-checking for your domestic sector (whether on one ticket or two). I am sure someone with recent experience can confirm.

With regard to lounges, there is no BA arrivals lounge but this board helpfully suggests there is a paid-for arrivals lounge with showers for (probably) ZAR300 per person: JNB arrivals. Again I don't know the details about gaining entry to the domestic SLOW lounge a long time ahead of your flight, but remember you are on a separate ticket not a connecting flight so you could be out of luck there.

I would personally go for the earlier option and accept I might have to pay for a new ticket or use some Avios if I missed the second flight (prices for flights today are ~£120). Or I would consider spending a longer layover in JNB and do a quick tour of the highlights before flying to CPT in the evening. YMMV.