Going commando isn't usually about sweat - it's most often about preventing more pressure points (elastic on underwear under compressive cycling shorts usually creates pressure points).

As for hair management.. I try not to shave the same day I ride. Unlike you, I do sweat, and sweat + freshly shaved skin = nightmare for me. I imagine the same would go for freshly waxed skin, but I haven't done that for a few years. I never let my pubic hair get very long, though, so I have never had experience with hair pulling..

If you search the forums, you'll find a lot of threads on these same subjects!