For the lowest conversion rates, try to use credit cards instead of cash for hotels and other charges when in a city. The card company will convert the African currency on your statement to U.S. dollars using that day's rate.
As someone above has said, you should alert your card companies that you will be out of country and check their fees long before you go. To that, I'll add that you see what they recommend to avoid identity theft in another country. You may want to consider a new card to use only in Africa.
Remember, airports generally are the most expensive places to convert U.S. dollars to or from an African currency. Ask your bank at home what its rate would be and buy your rands (of whatever) before you leave if the rate seems reasonable. If not, arrange to exchange your money at a bank at your destination.
Some outfitters may exchange the local currency for dollars, too.
Speaking of outfitters, long before you leave home, check with yours to see if he will accept a check for trophy fees, etc. Some will.
One final tip: Try to have US$100 in the local currency and 15-20 US$5 bills with you when you land You'll never know when you will need them for tips, taxis, etc.
Bill Quimby