Veterinarians usually clip hair from around a wound before bandaging it, but that doesn't mean the adhesive that keeps the bandage in place won't get stuck to your cat's hair. When it comes time to take the bandage off, you already have a safe solution on your pantry shelf to help with the removal process: Olive oil or another nontoxic, edible oil will dissolve the adhesive so you can pull the bandage from Fluffy's fur without causing her pain.
Pour a small amount of oil, approximately 1 tablespoon, into a shallow dish. Olive oil is ideal; vegetable oil and vitamin E oil are also safe and effective.
Dip your finger into the oil and dab it on the bandage, over the area stuck to your cat's fur. Repeat until that part of the bandage is saturated and beginning to loosen from the hair.
Hold your cat's skin and fur down with the fingers of one hand while you gently lift the outer edges of the bandage with the fingers of your other hand. Take your time to ensure that you don't pull your cat's fur. Gradually pull the bandage free, working from the outer edges in and adding more oil to the top and underside of the bandage as you go. Wipe away any excess oil with a rag.