Chain mail and Duct Tape.

You know how metal gives you that funny feeling when you bite it? If it does the same to the alligator, it may let go. If it does, grab the duct tape and wrap it around his jaws (or muzzle, whatever). They have a gripping power of 3,000 psi, but it's only for clamping down, not for opening their mouth.

Leave a good fold-back tab on the duct tape... that's not the time to be fumbling.

Sue