I see two problems and two "coder requests" for the custom-skinned player ships:
1) In Multi everyone has to download the said skins from each other --> not yet implemented in the code, so you'd need to manually distribute 'skin packs'.
1.1) --> Code request for automatic skin distribution through the host. May be a late 3.7 feature, but since you already have media for it, the coders will likely take the request seriously.
2) How do you make a mission use your own skin? It can already do this with squadron insignas, but so far only specifically FRED-ed mission with the texture-replacement sexp give you the ship you want...
...hmm, I think multi missions could be FREDed/scripted to use a "skin menu". You do an eval, key-pressed sexp, and if the player presses the appropriate button you display a menu with a list of availible skins. Press another key, and the game does a texture-replace sexp on the player's ships...
...now, does this sexp actually work on a ship already in the mission?
...and does it work in multi?
So many questions.
2.1) --> Another code request, also probably late 3.7 feature.