^ Also agreed.
Love the fast glass for critters, and close ups (like flowers).
You can't go wrong with a fast 70-200. I mean that's been a standard focal length speed lens for general purpose for what...going on 3 or 4 hundred years?
I disagree with the earlier comments about buying a single lens that goes from wide angle out to 200 or 250mm for two reasons. First, you already said you have a lens that covers the shorter focal lengths. Some will disagree with me, but the industry still needs to work on their one-size-fits-all lenses because what's out there isn't very good, IMHO. Second, these lenses are just soft in comparison to the fast 70-200 zoom in the same price range. Even though you said you aren't totally into this hobby, I'm sure you'll enjoy higher quality images that you do get with a better lens selection and since you're going on the vacation of your life and you'll be seeing some wildlife that you'll probably never see again in your life, why buy a lens that's gonna be a compromise when it's strength is the versatility that you don't need!
One final point is that I think since you're targeting the lens for this trip, I think I'd concentrate more on quality and focal length than speed...and since wildlife is a targeted subject, I do think having focal lengths longer than 200mm will come in handy. South Africa will have no under-abundance of light, so lens speed will be less of a priority, although from experience you're never sorry if you spend some extra for some extra speed (notwithstanding weight factors on bigger lenses).
I can't tell you how jealous I am of you. I've been to South Africa on business one time back in 1995 and it was the best place I've ever been...I'd LOVE to go back just for vacation.