The cone really just contains the flapping, which is distressing to a lot of folks. The actual killing of the bird is the same. Before we had a cone we just hung them upside down from a tree or whatever and slit their throats with a sharp knife, or grasp the head firmly and with a very sharp knife just decapitate the bird. Any way you do it you're going to have the bird flapping around some. But if the bird is upside down, it's going to bleed out. Or, if you do the old fashioned lay it on the stump and hatchet the head off, you just hold the feet and hold the bird upside down. You tend to get splattered that way, though!
Have you checked out the meat bird section? Lots of links to videos there, plus discussion of different methods. but be aware, folks can go on and on and on about the "most humane" way to dispatch a bird. Fact is, you're killing it and it's not going to like it, it's going to kick up a fuss. Even once the head's off it flaps around, and trust me it's already dead at that point!