In Storey's Guide, they suggest not removing the head because the chicken will aspirate blood which will toughen and taint the meat. They suggest a method called "debraining" as the quickest and easiest way to cull a chicken. Its not as bad as it sounds, and I have had chance to try both methods and do perfer this one. With the meat birds we are currently raising, I will be using this.
In using a hatchet you have to have steady aim and a strong arm. If you miss, have a weak stomach, or dont cut competly the first time, you leave a poor suffering soul laying there. In debraining, you insert a sharp knife up through the beak, through the roof of the mouth into the skull, and give one turn of the knife. The chicken is not only instantly gone, but if you are going to pluck and prepare the bird for eating, the debraining method causes a reflex reaction to loosen the feathers so they just come right out. It is next to impossible to mess up, as once the knife enters the skull the bird is gone and painfree. Dont mean to be gross, but if I weren't eating a bird, and simply putting it down to be humane, I would do this. Then I could bury my bird whole and mourne them.