I am not sure about whether or not this would be an option where you live, but you could just put the head down, place a .22 caliber pistol to the base of the skull (where it meets the spinal column), and shoot toward the nose. That would be a fairly instant death. I have not slaughtered rabbits that way, but I have done it to sheep, turkeys, and some other small animals.
Yeah, I agree with your neighbor. :P I have no problem butchering animals, but I cannot do it to animals that I raise. Every time I have tried, I ended up giving the meat away, because I felt so sick eating it. :P If you spend months raising an animal, you start to feel attached to it. :P That said though, I slaughter and butcher animals for my neighbors (for a share of the meat of course ), and I have no qualms about doing that. :P