I just did the same thing this past week. Flew SAA CPT-JNB on a separate ticket, with a checked bag. Then had a separate Delta ticket JNB-ATL. We had 3 hours between flights at JNB. Our flight was a little late (10 minutes) taking off from CPT due to traffic control at JNB.
Checked bags came out quickly but then you need to change terminals at JNB & the signage to do so is not that great. You end up walking partly thru the garage. We were in BE so we had a quick check-in at the DL ticket counter. We went to the club & had about 25-30 minutes before boarding was called (about 5 minutes later than expected).
Now, what did throw us for a loop was the LONG lines at the SAA ticket counter in CPT. We had not done online checkin. But after standing in line briefly, we figured out that we could get out of line, do online kiosk check-in, then walk around to the other side to drop our bags. This was much quicker.
One of our friends stayed in the ticket counter line and was told that they could not get on the plane because it was oversold and it was too late prior to take off. If she had not made that flight, she may have missed her JNB-ATL flight. It all ended well after she insisted on speaking to a supervisor. Surprisingly, her checked bag also made the flight.
So, you may want to be sure you also get to CPT with some time to spare, and/or do online check-in or kiosk check-in.