Short answer: Not possible.
Long answer: Not possible because it is not your video. Just because you appear in it and want it removed doesn't mean it is possible for you to do it on your own. You took the right step in contacting Facebook, and if you have not already I would suggest contacting the owner of the vid and asking to have it removed. In addition, if you don't want embarrassing things to get on the Internet, I would suggest not putting yourself in the position in the first place.
Assume that everything I say is or could be a lie.