I have read about Rhodesians joining the British armed forces as individuals and moving to "special forces" as I stress individuals, not as a unique Commando formation. One example appears to be recorded in: A Rhodesian Commando at War:Lieutenant-Colonel F.W. “Ted” Fynn (1939-1945) I exclude Rhodesians who formed part of the LRDG, that evolved after North Africa into raiders aka commandos.
I suppose you are already aware of this: The Southern Rhodesia Commando ‘Cobra’ Qualification badge – 1941 – 45 and of this: File:Rhodesian commando training at Gwelo, WW2.jpg - Wikimedia Commons