I wouldn't like to be the one holding the neck outstretched for your cleaver shot then Julie!

A lot of these mechanical dispatchers can also actually crush rather than dislocate and they are not recommended for humane despatch either under the poultry slaughter regulations.
I'm not a fan of messy cutting and decapitation methods, I prefer hand dislocation, brush handle, killing cone for larger stuff.
Saying that, they still recommend electrical stunning before and of the above methods too for a humane kill.

I have seen CO2 used successfully once on a small farm.
a pub gas bottle of CO2 piped into a small airtight container which held around 6 chickens , 2 feet square and 3 feet high with a cover over the top.
The chickens were placed into the container and lasted only a few seconds before being overcome by the CO2, they basically got back to their feet, had a look around and then dropped.
They were left in there for 2 minutes before being removed to ensure they were dead then the necks were also dislocated before they were plucked etc
That was a VERY calm and stress free method and something I may try myself one day, especially with larger stuff like turkeys etc.
The main thing I noticed with the CO2 was that there was no flapping and kicking like you normally see with other killing methods.
I also experienced large scale CO2 killing on commercial farms diagnosed with Salmonella just after Mrs. Currie's 1988 scaremongering campaign.
We used tipper lorries with their tarpaulins fitted over the top and gas piped in at the four corners.
The birds were then caught and carried outside by hand 4 at a time and dropped into the lorry (I was the dropper) and was tied up with a rope in case I fell in too.
A sorry sight but again it was an eerily silent and very calm method.