I completely decapitate with a SHARP! chef's knife. While it hangs from a scale, no cone involved. One hand holds the head, the other, the knife.
I do NOT recommend the technique to those new to the process, its very important that the blade be laid between vertebrae and drawn surely across the neck. Placement matters.
I will say, whatever method you use, that the chicken will move. Quite a lot actually. After it is dead. As in, I'm holding its head in my hand, the body is several feet away, and yet the wings are flapping, the blood is pumping out, and the beak appears to open and gasp. Completely normal, think nothing of it - no different than a lizard's tail. Closely related, chickens and lizards... Not cousins by any means, but more like the relationship between an ox cart and a Ford Model T.
Whatever you do, be swift and certain - hesitation does no one any favors. If a mistake happens, and it may, finish the job, THEN take a deep breath.