I would STRONGLY advise you don't even think about taking that much cash with you regardless of declaration requirements. That just has a potential of pain and suffering should "something" happen which could be as simple as just having it in a bag that somehow gets lost to more sinister things.
Some emergency cash for sure, like maybe a few hundred bucks. As Jim mentioned use your credit card otherwise unless you think you'll be somewhere that doesn't take a card.
I'd get clarification from your outfitter on this. I've tipped using U.S. dollars, the outfitter handled conversion with those receiving the tips. Perhaps yours can do the same and you can avoid the conversion to Rand hassle.
I guess what I'm saying is take U.S. dollars only and just enough to cover tips and a bit of spending money. Use your CC wherever possible. On that note call your CC company ahead of time to setup a "travel plan" with them. If you've not done this before, they certainly have. Provide them dates, destinations and relatively small amounts to approve for purchase.