Actually, yes you can.
In the "ahcache" folder, open the folder of the skin you want to become the default. Copy the .tca file from that folder into the "stdshape" folder and/or the "hirestex" folder, depending on the resolution you are using. Safest bet is to copy into both.
Now, you will see the skin you substituted as the default skin. You will see anybody flying in the arena with the default skin as being in the skin you substituted. If you disable other people's skins, you will see their plane as being the skin you substituted. However, if you are flying the default skin, other people will see you as flying the normal default skin, not the one you substituted.
Note: It's a good idea to back-up your default cache so you can revert to it.
I use this occasionally for immersion factor. For example, I put D-Day stripes and Defense of the Reich stripes on everything I can during June to commemorate D-Day and disable other skins so I see D-Day stripes on the majority of allied planes. (I know, Defense of the Reich does not necessarily correspond with D-Day, but let me have it my way!)
Regards,
Hammer