Halty,
I would have echoed the advice given above but on searching web came across this site -
http://www.flight-schools.net/airplane_rentals.html
This particular page says: "Please note that we deal with airplane rental companies throughout Southern Africa. You are welcome to contact us for your plane rental and helicopter rental requirements in countries such as Namibia, Botswana, Zimbabwe, Kenya, Udanda, Tanzania, Lesotho, Mozambique, Angola, Zambia and Swaziland, as well as in South Africa"
So possibly you could give them a try. I do know that validating a UK licence in SA is relatively fuss-free not so sure about how easy it would be in Botswana though.
All the best
GT