I seem to recall reading here on the forum that the golf carts are first come, first served, and that a tour guide (private or not) cannot "reserve" them. You will still need to go through the security line with everyone else. If you find a tour guide, determine if they will be responsible for your ticket purchase, which needs to be reserved, or if you will need to do that (ahead of time) yourself.
Have you googled something like "private tour guide for Versailles France"? With a quick look I saw several entries. I didn't check them out, but I did recognize a couple of the names of the companies. I would look at each one to see what they comprise, then come back to the forum with some names and data of ones that interest you, and see if anyone has an opinion on them.