"...a quick twist and a snap of the neck..."

I wouldn't try that. Without going into the gory (and painful) details, I once tried to do battle to the death, hand to hand, with a really mad Siamese. Cat's are tough. I once put down my cat of 19 years with chloroform (hard to get). Didn't work well. If I had to do it again, I would use a .22...