Perhaps you should verify with your vet, but IMHO you'd treat snakebite in a dog much the same as you would in a human: that said, there's an exhaustive and exhausting thread on snakebite ongoing here. I think the Sawyer has no role in treating either species for snakebite.

Ask your vet for 1 or 2 2" rolls of "Vetwrap". This is a somewhat elastic, self-adhesive roll bandage (Kerlix is similar). I've never had a bandage stay on a dog if only taped, so I overwrap with vetwrap much like an ACE bandage, if the wound allows.

My vet also gave me a vial of Dermabond for pad cuts. I've used superglue also.

A final suggestion: I've owned and/or trained some great dogs. Highly trained. They'd hold a "down-stay" and not nip, even when sutured. But even so, I'd always muzzle. You never know. And, people will be more willing to help you with an injured dog if the dog is muzzled....no matter how sweet and gentle you assure them your dog is.