If you look on the Humane Slaughter web page it lists ways of slaughter. The dispatcher is not seen as humane as it can cause suffering.
The stunning method is the most humane reported method but there are pros and cons. ( and I think you need a license but don't quote on that ).
I've been reading information and watching clips of dispatch for almost a year, trying to decide the best method as we wish to hatch our own hens.
We have decided that a pistol is quick and certain, followed by neck bleeding. OH has joined a gun club and is getting confidence practicing on rats at present ( the cockerels will be done at point blank ).
It really is a personal thing. Try to base your decision on how confident you are in doing it quickly and confidently. Always have a plan two in case plan one doesn't go to plan ( glad I learned this one from reading other's experiences ).
I have no experience in dispatch but am at the same point as yourself so hope this is of some help