Wondering what is your intention. Is this for future, dealing with larger birds, or dealing with youngsters. I don't know why, but I like to know these things. A very dreary subject, but must be talked about -- death is not easy, no matter which way we apply. You will hear many comments about methods, your choice to choose the one which you feel most comfortable with.
Cervical dislocation is my choice with the young birds, when that situation arises. Removing the head with something sharp is an action I take when the bird is bigger. PVC cutters are amazing, if they are sharp. I place the bird inside a feed bag, one foot on the top of the front of the back, my hand holding the head, the other hand squeezing the handle, instant. My foot helps to hold the bird in place. Once the head is removed I then can put my hands on the bird to hold it still. The mess stays in the bag. Sad to do this thing, but it must be done. I do not process my own birds, that is left to a professional to do that. I don't think I would be able to eat my own birds if I had to do the work myself, sigh...I consider a trip to the abbatoir a nice day out for a nice drive, coming home with some good food, smiling. Have a beautiful day, CynthiaM.