I am almost positive that the ArabellaSheraton has a resident car service (or a company they use) and that a trip from the hotel to the airport can be arragned while you are there with little advance notice.

As for a specific reccomendation, when I was in Cape Town in 2003, I arranged ground transfers from CPT to the Arabella Sheraton with the Southern Touring Company. I also used them for my sister's trip to Cape Town last year. They are very good, very professional and will take reservations via e-mail. Google them for their website, which will have their contact information.