I think I understand where you are coming from. My preferred method is to drive two nails to form a Vee in a section cut off from a large tree limb (like a tree stump), put the head in place and gently stretch so the target does not move, and use a hatchet. But I grew up swinging an ax, hammer, mattock, and hoe. I can hit what I swing at. I like the hatchet because it is lighter than an ax and easier to handle one handed but still has the heft to do the job as long as you can hit the target. A machete might take more arm strength if you are swinging it, which you are not.
One thing I’ve noticed is that it is easier to get a clean cut if the blade sinks into the wood a bit. It’s better to chop into the grain rather than across the grain.
Your method sounds like it might work better with three hands, one to hold the chicken, one to hold the machete, and one to swing the hammer. I’m not sure how close you can get the neck against the tree just hanging it from a string. I’d think you’d want the head firmly against the tree trunk. If you can’t swing a hatchet are you sure you can hit the machete with a hammer? I’d be a little concerned you might hurt yourself, let alone get a clean kill.
Your problem with the loppers is cleaning. Maybe your question should be more on how to clean the loppers? Do you think dumping them in a bucket of water as soon as you do the deed will keep the blood from drying until you are ready to clean?