It may disgust you, but decapitation can be done with one stroke in a split second with a sufficiently sharp knife (ever watch "Iron Chef"?). If someone cares enough for the animal, they can suck it up and get over their personal squeamishness.
Another method I like is "instant popicle"; i.e., drop in liquid nitrogen. If you know a large-animal vet that does AI on cattle and other livestock, they'll have a supply.
