Go to BYC for instructions. I have tried stretching out chicken's necks to chop, but I value my left thumb. I hang by the legs, slice the neck and and let them bleed out. Then chop off the head, skin to defeather, give the heads and legs to the dogs and eviscerate in my kitchen. You cut between where the legs where so you can get your hand inside the cavity, then work to break the membrane. All contents will slide out. I use the liver for gravy, give the heart, lungs and other organs to the cats or dogs, then toss the intestines, etc. in the trash. You feel very self sufficient when you dress a bird.
Ducks I don't want to even imagine how you'd put your thumb at risk when chopping, that's kind of scary to think of. One of my rules when dispatching a chicken or turkey is that I don't get hurt. Lot's of different ways to do these things and if you are happy with your method I'm not trying to change you.
When I dispatch a chicken or turkey I use the hatchet and stump method. I drive two big nails in to form a Vee, maybe 3/4" apart at the base and 1-1/2" at the top. That should work for a guinea. I hold the bird by the legs, put the neck in the Vee and gently stretch it out. Gently, not much pull. That holds the target in one place.
One trick I've learned with this is to always chop into the grain of the wood, not against the grain unless the log is pretty soft. I tried using a piece of 2x12 one time and the hatchet bounced off instead of sinking in and taking the head off. It still worked but it wasn't as clean a kill as I like.
Sprig, how much experience do you have processing birds? I've never done a guinea but other than maybe the feathers I can't see it being much different than a chicken or turkey.