What? :-o
IIRC, you can upload to lfsworld fake skin (which will be shown to other players when online), and update local skin file on your disk, so you will see your correct skin on your computer = problem solved.
If you want others to see your skin, you are making it technically public, the data are available. Decent people will respect your wish to not use it, if you say so, but there is no way to have both display of skin, and not providing data of skin, at the same time. (and "dds" doesn't prevent anything, you think it's difficult to convert it to other formats?)
Or don't use custom skins at all, it's just look of the car, who cares...