I'm not sure what cone method everyone is thinking is complicated or takes a long time?? I must be missing something. When I had a cone, I had it nailed to a beam with a bucket under it. I put the chicken in, the head and neck come out the bottom. I took a machete and decapitated it. Exactly the "hatchet" method, but no fussing with stumps and nails and aim and flailing, just whack and done. Honest truth, I usually wrap the head in a paper towel as soon as the bird is in the cone - it never sees anything and I don't have a head staring at me from the bucket.
Lacking a cone, and having enough hay twine to macrame the entire farm, I take a loop of hay twine, put one end through the other, put it around the chicken's ankles (individually if it's a large bird) and hang the twine from a hook on a beam and do the same thing, but without a cone. There's not a huge amount of flapping, but if it disturbs you, cones are easy to make. Before they were a thing you could buy, people used old traffic cones and corners of sturdy burlap feed sacks before that.