So what my little bit of research shows is that one of the possible way to change skins would be to change the skin name in an override file, though... well, that way doesn't work. At least for me. It's still the default skin.
Replacing the texture itself from an external pk3 or changing the default skinfile so it points to a non-default texture works for me, though that kind of defeats the purpose.
I'd love to hear some explanations or at least 'you're doing it wrong' from the devs.
P.S. I did all the testing on my main box, which (for now) has only an ES1000 for graphics, and that means a fully in-software 3D rendering at slow speeds and with bugs. I'll check this on the other computer too ASAP to check the real outcome.