Seems like you have the setup for a cool idea right in the opening post. If you're using stuff like Greek gods, why not say your character's a demigod (whether she knows it or not)? She's may not be skilled, but just so damned strong that normal weapons crumble in her hands, so she just uses her hands! Maybe a Four Elements monk could be a child of Posiden or Ares or something, or the shadow monk could be related to Hades or Loki.