Using carbon fiber as a core is an abuse of the material. Not that it would break, but it's much heavier than what you need. If you insist on using carbon fiber, then two perpendicular layers of the thinnest pre-cured carbon uni on each side of a light weight core such as foam or balsa, of greater thickness, would be MUCH stiffer and probably lighter too. Of course, in this case, such construction would be overkill. It's pretty easy to sand a foil shape into balsa or foam. If your rocket is going trans or supersonic, my guess is you still need to keep the fins thin. maybe 5 mm at the root, and thinner at the tip. 5 pecent thick foil sections? Maybe something that looks like a symmetrical foil from the NACA 65 series. Someone who is more knowledgeable about compressible flow could chime in here. For a subsonic rocket, you could probably make the root section as much as 10 percent thick without much of a penalty. Making the fins 3 times thicker at the root is going to do wonders for their stiffness, and make them considerably stronger, too. If you are concerned about local dings, you could slot the leading and trailing edges and inlay a strip of your carbon. Or thin plywood. The trailing edges can end cut off square, and if you make them less than knife sharp, that will only hurt a little.
If it was me, I might just sand some airfoil shaped fins up out of balsa, and apply two layers of light glass, one with the weave at 0/90 and the other at +/- 45 degrees. If I could figure out a reliable way to glue it down, maybe use the metal from an aluminum can, which is close to equally stiff in all directions. If you want to get fancy, you can use the following technique, though the airfoil shown is obviously inappropriate:
https://charlesriverrc.org/articles...ithout-templates/markdrela_airfoilshaping.pdf
Professor Drela is kind of a genius. On the other hand, you can get fine results by eyeballing it, casting straight edge shadows on the surface, or drawing straight lines. Even a quick hack job will be better than thin, rectangular cross-section fins. I'll attach a picture of the NACA 65-006. Keep in mind that you can make the trailiing edge a little thicker without a severe drag penalty.
