You can only see the default skins in the skin viewer, or skins that you have downloaded (from ah-skins.com or any other page) and/or created yourself. You won't be able to view the custom skins already in-game.
The cache rebuild is a bug we've had for a while. The skin viewer file needs to be updated to fix this. Nothing we can do about it.
If you don't want to rebuild your cache, you can always simply view a skin offline in Aces High. Anything the film viewer shows you, you can also see in Aces High itself. The viewer just lets you view it from easier angles.