It seems that there is no way to change the race of your character without at least doing the same to every other character, but this random arena video
WarcraftMovies.com - World of Warcraft Movies
shows after the first minute an UD male changed into a dwarf. His teammate and opponents, all UD males, were unaffected.
Later on it shows a match from his teammates perspective which shows him as a dwarf, though the teammate was still undead. I'm really confused by this, does anyone have an explanation? o_O