The colors will more than likely dull considerably. It might not be a bad idea to use some translucent pigments over the skin before the final finishing. Mixing paint with clear coat can get you translucent paint. That's very similar to the way taxidermists paint fish mounts. I considered getting into painting fish mounts at one point, just because I had the airbrush experience already, but never got around to it.
I have never used fish skins on a bow so I have no advice on how to prep them. Several members have, so hang in there someone will chime in.