A towel is very helpful because it pins the wings into the body and keeps the bird calm. It also stops the death throw flapping. But you need to hold onto them the whole time until the heart stops. Its a really peaceful way for them to go.I can hold a chicken by the feet & wingtips with one hand, leaving the other hand free for the ax (machete, cleaver, whatever cutting tool.)
But if you need one hand for the knife and another to stabilise the head, then it might not work for you.
I've read of people wrapping a chicken in a towel, and then wrapping a bandage around that to hold the towel in place. It's commonly recommended when the bird is injured and the person needs both hands to treat it, but would probably work fine for killing as well.