Hi
People do cycle around SA without a police escort.
There a couple of travelogues about individuals who are currently cycling across Africa, and are on their way to SA, in our travelogue section here,
http://www.africaguide.com/travelog/index.htm
What you might want to do is contact them and get an idea of any problems they have encoutered.
I was travelling in a vehicle around SA last year and was told numerous times about how dangerous it was - warned that I might get held up at gun point if I stopped at the red lights .. and it does put you off when you are repeatedly told about the dangers.
However, I didn't encounter any problems and never felt threatened and I loved the country and I think cycling round would be a fantastic experience.
If you take sensible precautions you should be ok... no night cycling, no free camping etc... Admittedly it is risky - but it does depend how adventurous you are on whether you go or not...
Whats the difference between walking round and cycling... and people walk around every day. Yes there are muggings etc... but where in the world isn't there??