I did exactly what you described. I spent 30 days doing volunteer conservation work, mostly in Botswana, but also spent a decent amount of time in South Africa. I added on an additional few days in-country to do some more personal stuff (a safari).
Calling it volunteer work is a bit of an oxymoron. More like pay-to-volunteer work. There are no "free" programs, especially for primates or the big cats. You have to pay, a considerable amount, for the privilege of "volunteering." In fact, it was by far the most expensive month of my life, and I could have bought a car for what I paid, although the safari cost a considerable amount (absolutely worth it).
It is essentially a great way to see "wild" Africa, not entirely as a tourist. I would recommend it, but make sure you understand what you are getting into. These programs do not need volunteers to help with serious scientific work. They need rich Americans to pay them what is a small (maybe large) fortune in Africa, for the experience of being in Africa and perhaps aiding a bit with some research. There are several outfits that rely entirely upon "busy work," work that does not need to be done and that serves no purpose to anyone, to keep their paying "volunteers" busy. I know of one outfit in general that does daily game counts in a fairly small area, and while this is interesting to go along on, the data gathered is of use to no one, and most likely is not even reported.
Overall it was a positive experience, but I have always been fascinated with Africa. I intend to return many times, although not for conservation work. Feel free to PM me for additional details, such as the operation I went with.