Ideally, your surgery would be done under twilight anesthesia to avoid the need for a breathing tube. This would significantly decrease the irritation and subsequent swelling of your vocal cords. The most significant hurdle would be the normal stiffness that comes from face and neck swelling. I would recommend waiting at least 2 weeks and then beginning slowly as tolerated. Best of luck!
If you are undergoing general anasthesia,you may have a tube down your throat,so this will cause some post op swelling of the vocal chords. I usually place my patients on a short course of steroids if this is a problem.You don't want to strain your vocal chords