I've do this trip multiple times a year in both directions, same ticket as you indicate. SAA should be able to provide you with the CM boarding passes in JNB or wherever you start your journey with them. The transfer at GRU is painless - just a light security check upon arrival, they either ask you for the BP or a printout of the ticket. SAA arrives at Terminal 3, Copa departs out of Terminal 2 - both are connected airside thru long corridors.
One item though if you plan to check luggage. Although possible thru interlining, I´ve learned the hard way to avoid checking the bags from South Africa all the way to your final destination if your connection involves GRU. Have had luggage lost for several days. Possible reasons is because we are talking about a bag transfer between two different airlines, located at different terminals in a non-hub airport for either, that use different baggage handling companies with no overlapping working hours, and a long layover for your bag to be sitting around.
What I have done is ask SAA to tag the bag just to GRU. At GRU pick up the bag, and wait landside. At the time SAA's flight arrives, there is no one at immigration nor customs, so it is at most a 15 minute process from gate to arrivals hall. The caveat is that Copa's check in does not start until 2-3 hours before departure, so you would end up spending 8-9 hrs with your luggage at hand. While bearable, waiting landside is much more interesting than waiting airside at GRU Terminal 2, which is a dump airside. I´ve used the hotel outside arrivals in Terminal 2 (Copa's terminal) where you can book rooms on hourly basis or overnight. Great place to leave your suitcase, rest and shower. In any case, by picking up the bags at GRU, reduced the chances of lost/delayed bags have saved me lots of stress/grief at the end of a long journey.
Regarding yellow fever certificate, Copa has never asked me for one, especially given that you're not entering Panama and are just transferring thru there. Even when my final destination is Panama, never been asked to produce one. They can check the itinerary that I did not started my journey in Brazil.