An old farmer (a neighbor) told me something that stuck with me. "Jen, if you own chickens... own an axe. It doesn't matter what size the chick or chicken is, you don't want to hunt around for a way to do it when you really need it." I got to thinking about that. Seriously. I had to cull a chick with a broken pelvis a month ago, and was glad I had taken his advice. It's quick, very quick, and now I have the axe in case I someday wake up and something's gotten into the chicken coup that left really seriously wounded chickens that needed culled immediately.
Just get an axe and be prepared to use it. If you own animals, you need to take responsibility for those animals and not get someone else to do your dirty work for you. Sometimes its a true kindness in the culling.