Done the Jberg overnight layover a good number of times. Twice last year (2022), June and Aug. June was to Namibia, Aug to Botswana. Delta over and SA Ailink from Jberg to Windhoek and Gaborone.
Two major factors: a) are you flying on a "contiguous ticket". Meaning, is your long-haul flt from the US to Jberg and your flt from Jberg to, in this case Windhoek, on the SAME reservation code or are you flying on "split tickets". Meaning one airline ticket and reservation code to JNB and a separate ticket and reservation code from JNB to WDH with SA Airlink? IF, you are on a contiguous ticket, when you check-in with the first flight you're checked luggage and rifle case and ammo should be able to be checked all the way thru to WDH. Good side of this is you don't have to screw with the SAPS 520 form and the SAPS office dick dance. You just have to plan your carry-on bag for your overnight stay accordingly.
b) IF you are on a split ticket and your primary airline has a baggage handling agreement with SA Airlink or other regional African carrier, when you check-in for your first flt, IF you show both tickets to the check-in agent, AND they are feeling agreeable, they can check everything all the way thru. The next morning you'll just need to collect your boarding pass from SA Airlink desks in the main hall. When you do, MAKE SURE you give them your baggage claim tickets so they can be sure your bags/rifle cases are on the aircraft loading manifest. You'll also have to pay a nominal $35.00 US fee for EACH rifle in your case.
Coming home, same thing. When checking in, show both tickets to the agent and they should be able to check your luggage/rifle case and ammo box all they way back to your US Port of Entry. Collect it all up, clear US Customs and then you'll need to re-check it all to your final destination. Your US Port of Entry airport will have a baggage transfer area so you don't have to go out into the main hall.
Examples: On my June 22 trip two of us flying Delta to JNB. I originated out of Tampa, friend out of South Carolina. Both traveling on "split tickets". He showed both to his check-in agent and all his was checked all the way to WDH. I opted to claim my stuff in JNB, mostly because I don't trust anything being left for a long time there.
Just to be certain, I did have SAPS 520's for both of us filled out and just needed to be signed. He obviously didn't need his and I did. His luggage and rifle case pitched up just fine the next day in WDH. Coming home, SA Airlink agent checked us both all the way to Atlanta but, I still had another set of filled out SAPS 520's for us, just in case. We again, just had to pay the gun handling fee. We also confirmed our baggage claim tickets
I did a solo trip to Bots in Aug 22. Same deal, split ticket Delta from Tampa to JNB and SA Airlink next day to Gaborone. This time, showed both tickets and checked all the way to Gabs. Same drill. next morning got my boarding pass from SA Airlink, confirmed by luggage claim tags, paid my fee, got my boarding pass etc.
Same drill coming home. Checked all the way to ATL, paid my fee in Gabs, confirmed my baggage claim tickets in JNB.
BUT, I STILL carried two sets of completed SAPS 520's just in case.
One more general caution. Your US carrier to JNB usually has a 50# free checked bag limit. However, SA Airlink is 40#. IF you claim your bags in JNB and re-check in the morning and your rifle case and checked bag(s) are over 40#, you'll be paying overweight bag fees as well.
Sounds like you've already booked your tickets. Just be 100% sure that the airlines you've got from the US to JNB will carry firearms. I think currently, there are only two US carriers that fly direct from the US to JNB, Delta and United. They are both firearm friendly. As a general caution to all, there are several international carries that do NOT allow firearms or have layovers in countries that don't allow firearms to even transit.
To the OP, as others have mentioned above, if you have limited experience traveling internationally with firearms and transiting JNB, it would be a VERY good idea to hire a transfer agent/meet and greet service. There are several, all are about the same price. EVEN IF your firearms are checked all the way thru, they will still meet you at the gate, walk you thru RSA Immigration and IF you're overnighting in the airport terminal complex, escort you to the hotel and meet you the next morning and make sure you get on your next flight.
So far, I'm taking three guys with me to Bots this Aug. Split tickets purchased (Delta/SA Airlink). Same drill with an overnight in JNB at the City Lodge Hotel. All of us flying out of Tampa and hopefully, checking luggage and rifle cases all the way to Gabs. I will STILL have copies of pre-filled out SAPS 520's for each of us for each way, just in case.
This all may sound scarier/more complicated than it is, once you've done it a few times.