That is a very delicate operation. The carbon would be visually the same as a clearcoated carbon. The precarious thing is how to remove the paint without damaging or touching the fibers. I cannot reccomend a chemical means, but that does not mean it is impossible. Contact a place that deals with carbon fiber construction or the frame manufacturer and ask them if there is a compatible chemical stripper. If it is not, it can soften the bonding agent and compromise the frame.
The other option is to get some finer grit sandpapers. Start with 220 grit and sand lightly while keeping it wet. The water allows the work to come out smoother and keeps the paper from clogging. When you feel like the color is almost off, switch to a finer grit. 400 or so and procede, still wet, and take the remaining color off. Follow that with 600 grit very lightly and dry it off after you rinse it.
Look for scratches that may have been left from the sanding. It is important to remove these as they can be problematic later.
To get the best results for a clearcoat, get some Gelcoat from a fiberglass/carbon fiber finishing supplier and follow its instructions for application. You will not need or want much, but it will come out much better than a paint type clear.