Thanks to everyone who's contributed to this important discussion. I can't kill anything, and I think it's a serious failing. I've had a several ex-battery hens and though it is wonderful to see them recover there inevitably comes a time when they go downhill. I've had a couple die when it probably would have been kinder to put them down sooner, I've asked the vet to do it for me (at unwelcome expense), and I got a friend to kill one for me. I don't like any of these solutions. I should be able to do it myself.
In the end I found this article and video which has helped me come closest to the idea of actually doing it myself.
http://peterdickinson.hubpages.com/hub/How-To-Kill-A-Chicken
I guess it's pretty similar to the broomstick method. I'm sure people who've suggested doing it at night are on to something. They're so much more dopey then.
I still haven't done it myself but I'm getting closer. I dread being able to feel the sensation in my body for days afterwards. But it is part of our food system, unless you're completely vegan. Better to know it's been done humanely, however unpleasant, than to outsource it to who knows who or how.