It doesn't compare to butchering an elk, but it is back on the chicken track: I worked briefly as a teenager at a large commercial poultry, I can't call it a farm, let's call it a production center. One of our jobs (in addition to shovelling out the droppings of around 6000 chickens each day) was to "euthanize" injured birds. We found the quickest and easiest way was to get a good, comfortable grip on the chicken's head with one hand, lift and and make like the bird is a New Year's noisemaker - give it a few quick spins. It snaps the neck quite efficiently and certainly doesn't cause any more pain or suffering than any other method. And at that point it is possible to tear the head off and let it bleed out, although that takes a lot of twisting and pulling and is definitely not for the squeamish.

I learned a few summers later that by starting at the legs where the skin is a little thin and loose, with a little finger strength you can actually skin (more like peel) a chicken without a knife. It's not as easy as with a rabbit, but you can do it. It's hard to get the wings out intact, though.

Compared to that, doing it with an SAK would be a breeze. As has been said, a sharp paring knife is better still. But it just goes to show what can be done if one must, as in a survival situation.