You can try it on an old hose or even a rope. Practically any hatchet or cleaver will work, though I'd like to see a scaled photo of the cleaver just to eliminate some guesswork on that. I don't like to assume. A heavy cleaver is good.
The issue is going to be you. Can you hit the target with enough force. The rope or hose is more about hitting the target than generating enough force. If you hit it cleanly you don't have to be a body builder or weight-lifter to generate enough force. Rope comes in different materials and may be harder to cut than a chicken's neck, not sure. An old garden hose may be closer but probably takes more force than a chicken's neck. Remember, you do not need to totally take off the chicken's head. You need to cut the spinal cord to kill it. And you need to keep your eyes open so you hit the target. If you flinch or close your eyes at the wrong time you can injure the chicken or yourself.
In my earlier post in this thread I mentioned the grain of the wood. You want the hatchet or cleaver to cut into the grain of wood, not across it. If you cut into the grain, like a stump, the hatchet or cleaver will sink in, giving a cleaner cut. If you cut across the grain, like the side of a plank, the hatchet or cleaver may bounce back and not get a clean cut.