Well ... If Sinestro (in Hal's body) can GROW a mustache ...!
Agh! That's not right. That's DEFINITELY not right.
Still, despite the fact that Oliver (Green Arrow) Queen -- the whisker king -- is one of Hal's best friends, Hal himself doesn't seem to be a big fan of facial hair. So, if Hal was trapped in Sinestro's body, OF COURSE he'd shave off Sinestro's mustache!.