I was there a few weeks ago. If you do book excursions, that's cool I met one couple who did so. But I don't think you need to for all of the things you mention.
1. Many people rented cars, you might consider getting one as it was very common.
2. Table mountain: Close to the city, easily reachable by taxi or bus. If you look into other posts here, the MyCiti bus is very usable and runs to the airport and seems pretty safe. The mountain ride closes if it is windy. Check the reports for weather, and usually the mornings have the best visibility from what I understand. On my trip it was closed in the afternoons on the first two days I was in CPT. Our shark boat captain said they sometimes close it with people up on top and they have to stay the night at the lookout. I don't know if that is verifiable, but when you get to the top keep an eye out for weather too I guess and head down if it looks bad. Buying your ticket online for this should save you time in the queue for tickets, but there is still a queue for the ride itself.
3. Shark diving: For booking, the company you choose can provide a pickup either one way or round trip for an additional fee. I used the one way pickup, since it is an early morning start. It was around $35 I think one way, and $50 RT. Going back to the city, I took the train. It allowed me to walk about a mile to the Penguin beach, then about 1.5 miles back to the train station, and the train is about an hour ride and less than $3. I did all my booking for the trip and the ride through email, and found the train info online. Some people on my boat had cars, and others had arranged for their driver or their hostel to pick them up after, so I don't think this should be hard to arrange. I think you can combine the Shark Dive with a wine tour as they are both outside the city.
For choosing your dive, there are two areas for shark dives. I went to Simon's Town. It seems more famous, but it was a big mistake. The websites said it was open earlier than usual this year. Unfortunately earlier than usual did not mean that it was near normal. My boat didn't even let anyone in the water, and right away after leaving the dock the captain said he didn't think we would dive he just hoped we would see some sharks. I was not pleased, as I had no desire to just go on a boat ride. It was extremely windy, the day before and after me they did not even go out. We did see one shark for about 30 seconds. They gave vouchers for a free trip another day in a year, or offered people around 40% off. Your time of year it might only be one or the other available, but my advice for this is email and ask lots of questions about what is going on and if they are diving or just viewing etc. and choose between Simon's Town and Gansbaai after lots of info and communication. The company was friendly and easy to talk with, and was honest about the weather. I was not able to go a different time of year, but I should have gone to Gansbaai instead.