First you can take the easy route and simply cover the scratches with a clear coat to protect them. After coming across a diy carbon fiber repair kit on amazon i decided to try my hand at fixing my frame.
How To Repair A Scratched Carbon Parts
Repair carbon fiber scratch. 1200 carbon fiber drop out replacement. I ordered the easy start kit from a company called gorilla carbonworks on amazon. With clear coat and some time sounds like maybe a 20 fix. 300 350 most common damage. Diy carbon fiber repair kit and step by step tutorial duration. Not structural but ugly supplies the resin and hardener included in the kit.
If the scratch is very light however i would try first with the polishing compound alone see how that comes out before any water sanding. Videos can be found on youtube showing how to repair the frame. Composite dimensions 189346 views. I have repaired real carbon fiber motorcycle gas tank protectors with light scratches by lightly wet sanding with 1000 grit paper to get rid of the scratch followed by polishing with a rubbing compound. The 40 kit includes a 39x6 sheet of 3k. Since it sounds like your fix is cosmetic and not structural you could probably get away with just putting a layer or 2 of that down to cover the scratch.
The size location and severity of the damage affects the cost of repair. You should question using nail varnish on carbon bikes as there are reports that the chemical format can degrade the resins used to bond carbon fibre. Carbon fiber is just fiber and epoxy layered together. Some use high quality chip free nail polish clear coat such as cnd speedy clear coat. Depending on the ferocity of your scratch and the level of your resolve to repair it you have a couple of options for getting that shine back. With a light cosmetic scratch the panel can be clear coated to hide the scratch.
Iirc its something like 12yd. Theres a fabriccraft store near my end of the world that sells legit carbon fiber weave by the yard. 50 addreplace h20 bottle bosses cable stops etc. If its simply the lacquer which has come off then you can replace it with the lacquer from a car touch up kit. Its a really expensive glue sandwich. A look at the damaged area.
As an example if a corvette has a visible carbon roof that is scratched a repair can be made if the roof will be painted. How to remove scratches on carbon fiver accessories. 400 soft squishy holes full breaks joints damage. That scratch is not going to affect the bike in any way but if its making you crazy you can try putting something like epoxy paint nail polish etc on it and then sanding that until it matches the finish on the bike. But if the carbon fibers are torn a repair patch would be visible and not acceptable to the customer. To give you a rough idea of costs 250 small cracks and dings.