If you simply can not bring yourself to cut its head off, you may want to try what I read a couple of people did on this forum last year. It sounds very odd, but it was the only way they could bring themselves to cull a chick. They put it in a box, tucked the box up against the wheel of the car, and ran over it. The death was instant. I know it sounds bizarre and I was almost appalled when I first read it, but after reading pages of them agonizing over how to cull a chick, I realized this was the only way they could do it and not have nightmares. I know of at least two people that culled this way.
Whatever you decide, I wish you the very best of luck. Culling is never a pleasant thing, but it is sometimes the right thing to do.
Penny