If you can't through check bags, then you will need to clear immigration, collect your bags, pass customs and then recheck. The good news is that Airlink have a recheck desk just after customs and before the main public arrival hall. However I don't know whether that will handle international rechecks...but even if it doesn't you just head up a couple of levels, walk towards Terminal B and you will find the main Airlink international check in desk. Both Terminals join together airside so there is no need for shuttle buses or any nonsense.

Assuming you have 3 hours you will have plenty of time for this. People seem to treat JNB as if it's a mini-Lagos. In reality it works pretty well almost all of the time.