I would use a towel to gently wrap around his wings to restrain him. You might have to gently tie his legs together or wrap them in the towel as well to keep him from using them to fight. If you are able to use a head lamp in an otherwise darkened room, that might help keep him calm.
Using the diagram posted by @Wyorp Rock it will probably be helpful to figure out exactly which areas you're going to work on. Keep in mind that you may need to change up the plan as you go and are better able to assess more.
Using the diagram posted by @Wyorp Rock it will probably be helpful to figure out exactly which areas you're going to work on. Keep in mind that you may need to change up the plan as you go and are better able to assess more.