When my Liddy broker her toe the more wrapping I did, the more problems it created. My vet gave me an antibiotic powder to help keep the would dry and honestly, the less I wrapped the wounds the better it got. It is keeping the dog from licking the wounds that is the objective (but they say their saliva has good enzymes to help clean the wound??). I was fortunate to be a stay at home mom to my critters both skin and fur. I supervised her 24/7 until she could be alone and then I would dress the wound with a baby sock and a little tape to keep it up (loosely) and use one of those e-collars when I was not near her.
Best of luck, it is a difficult challenge.