Carbon fibre has good tensile properties, so it is best wrapped around an outer convex surface where tension forces in long fibres will not cause delamination. Internal concave surfaces tend to be compressive so it is the glue or filler that will be more important, held in place by short fibres as reinforcing.
Small plastic items break after becoming brittle with time. I sometimes repair them by reassembling the parts with cheap superglue. Then I wind a Kevlar fibre around them, backwards and forwards to make a very thin outer sock of cross-hatched thread. One drop of fluid superglue on the Kevlar wicks through to make a very strong exoskeleton. The superglue, = cyanoacrylate, chemically bonds with the Kevlar, = aramid.
I get the Kevlar fibre from scrap cable. Make sure you are not touching any fibres as the superglue wicks in, or you will very rapidly become part of the exoskeleton.