Personally, I think it is the flapping that is so destressing to people, even though I know the animal is dead, it seems so alive. One is secretly afraid that they have made a mistake and it is not dead after all, which is horrible because now you have to do something again! ugh! It is one of the reasons I prefer to go with the slit throat, if the knife or blade is sharpe, they don't really notice it, and they mostly just get tired and weak.
But I was quite impressed with the rabbit deal in the video above, wow, quick!
So if you can wrap them up, it will help.
Mrs K