Move him to moist paper towels. No dirt is really all that sterile. The dirt can also impede the healing process.
Worms are not really an appropriate diet for a Garter Snake. I would pick him up a few Silversides or Guppies. You can also scent pinkie mice with frogs or minnows, sometimes they will take them. Remember to stay away from all members of the Cyprinidae family (Carp). They have a enzyme known as thiaminase, which prevents the absorption of Thiamine (Vitamin B1). Which can cause serious health problems, possibly being fatal.
I would make a betadine or nolvasan rinse to rinse out the wound, cleaning it throughly. Then place a bit of polysporin on the wound and it should heal. I've dealt with much worse and had a positive outcome.
Good luck.