When I'm getting ready for chicken slaughter day I'll typically use my electric poultry netting to constrict them to relatively small space. You can have it hot, or not, the couple that usually escape if its not hot haven't been that big of a deal to catch. Granted I often have quite a crowd, so there's usually someone taking a break that can chase them down if necessary. And not energizing the
fence makes life nicer for the people interacting with the
fence.
What can help a lot for chickens (and I'd assume ducks too) is to have a "chute" that you herd them into. I made a rectangle that was maybe 3-4' wide and about 8' long with welded livestock panels or no-climb fence for the long sides, covered in a tarp, and a fence gate for the short sides. The tarp is very helpful especially with welded livestock panels as the openings are too big to contain the birds on their own. Plus having a visual barrier helps keep the birds calm. Having a kid inside the chute to hand birds to whoever is running the dispatch station works pretty well as long as said kid knows how to handle them. A couple/three kids to herd 10-15 birds at a time from the main area made with the poultry netting into the chute keeps things from getting too crowded, but also keeps things moving along.
For lambs, a square or triangle of the welded livestock panels (depending on how many you're wanting to corrale) inside the main paddock for the rest of the herd, secured with decently beefy zip ties at each corner, allows the lamb to still be close to the other sheep if it's just the one you'll be butchering until you're ready to do it. Note that you'll definitely want to set a T-post at the corners (and/or use fixed fencing for one or two sides) as otherwise the lambs will just push the panels around the paddock. For lambs you'd need to skip the tarp covering. They would need to be able to see their flock mates in order to remain calm. Remember that sheep fear separation from their flock far more than death itself. You can cut the lambs throat in full view of the other sheep without problem. With goats you would want to shield the remaining ones from view of the actual kill as they're smart enough to remember you doing that. But sheep generally don't care.