I would rinse with cool water, gentle stream, as the vet instructed. It will help cool off any swelling and rinse off pus and debris. Then I would put any topical antibiotics on there that the vet told you to (I'm assuming that he's having you give antibiotics by mouth, though). Then I would put the honey in a small squirt bottle (e.g. like a honey bottle!) or an empty wormer tube with a tip, and gently apply it along the edges of the wound, letting a little drip down into the gap below the skin flap. Stan's in summer in NZ and he's right about insects. Here in the US Midwest, insects are dormant right now so I wouldn't cover unless you're dealing with flies in NC already.
Honey is a natural antibacterial, suppressing infection from bacteria. The manuka component, from NZ tea trees, has an unusual healing property as well that goes beyond what antibiotics can do.
Proud flesh can be a problem with any wound, but it's aggravated by movement (e.g. the reason for stall rest), irritation or rubbing (the reason for not scrubbing) and just slow healing in general (don't go overboard with trying ointments or other stuff as too much of a good thing can be bad). Pressure dressings can keep proud flesh under control by forcing the edges of the wound to be flatter, which helps the baby epidermis cells spread across the open wound.
You'll have 3 steps forward and 1 step backward no matter what you try, so as long as healing is headed in the right direction I'd stick with the plan.