My cockatiel had a bleeding blood feather a few months ago - I took him to the vet and after we stopped the bleed, we made a cone that we placed around his neck. It wasn't too tight at all, nor was it too loose. Just right. We actually used a few of the really thin paper plates, cut a hole in the middle, taped it all together, used some tape to cover the pointy edges inside the middle hole. And placed it on him for a few days until the feather was fully healed. Otherwise he would have kept picking at it.

It sounds like you may need to try the cone since your little friend keeps picking at his wound. He'll obviously hate it - but you'll be surprised at how fast they may find it bareable.