0wen
Songster
If you're uncomfortable with a hands-on approach - axe, dislocation, etc, I would suggest looking into controlled atmosphere euthanasia. Some links to information, discussion, & videos. Absent this method, I would recommend a high powered air rifle .177 or .22 to the head.
https://www.backyardchickens.com/t/934727/nitrogen-euthanasia
https://www.backyardchickens.com/t/14845/diy-humane-way-to-kill-slaughter-chicken-stun-kill-gas/630
http://www.peta.org/features/case-controlled-atmosphere-killing/
https://www.hsa.org.uk/downloads/technical-notes/TN12-gas-killing-of-chickens-and-turkeys.pdf
https://www.backyardchickens.com/t/934727/nitrogen-euthanasia
https://www.backyardchickens.com/t/14845/diy-humane-way-to-kill-slaughter-chicken-stun-kill-gas/630
http://www.peta.org/features/case-controlled-atmosphere-killing/
https://www.hsa.org.uk/downloads/technical-notes/TN12-gas-killing-of-chickens-and-turkeys.pdf