If non-traditional means not-traditional-to-western-cultures, then the one I've come close to would be sitar. I've so far taken one "lesson" (a workshop with Sandip Berman, fantastic tabla/sitar/voice player who has toured with Bela Fleck among others) and the gentleman was nice enough to offer to let me use his sitar to practice on.
I'm not sure I'm cut out for sitar though, they are quite challenging to play, even physically.
Maybe Hawaiian lap steel?