Catch them when they are settled
Ducks are creatures of the ground and the evening. By dusk the flock has usually gathered, fed and settled, and birds handled then are noticeably calmer than birds chased around a pen in the heat of the day. Work in the last of the light or just after dark if you have help and a torch, and keep voices low and movements slow. A duck that is grabbed at after a long chase arrives at the crate already panting and stressed, and a whole flock worked up together can take hours to settle again at the other end.
Herd rather than hunt. Use hurdles, a length of netting or a couple of helpers with outstretched arms to walk the flock quietly into a corner or a small catching pen. Ducks move willingly as a group along a fence line, and a bird that walks into the corner with its flockmates stays far calmer than one singled out mid-pen. Pick each bird up with both hands, one over the wings to keep them folded and one supporting the body, and never lift a duck by its legs or neck.
Crate in small, counted groups
Use ventilated crates or sturdy boxes with dry bedding in the base, sized so birds can sit but not be thrown around. A few birds per crate is better than one crowded box: overcrowding builds heat fast, and ducks overheat more readily than they chill. Keep drakes that scrap in separate crates, and keep a duck sitting on eggs or raising ducklings with her little family together rather than mixing her into the main group.
Count out loud as each bird goes in, and write the number on the crate with a marker. Then count the crates themselves onto the vehicle. It sounds fussy until the day a crate is left behind in a dark pen — the written count is what turns "I think we got them all" into certainty. Load crates level, wedged so they cannot slide, with air able to move between them, and cover the load if the journey is breezy so the birds travel in dim, draught-free quiet.
Set up the new pen before the birds arrive
The destination does half the work of a calm move. Before the ducks leave the old property, the new pen should be fenced, checked for gaps at ground level, and stocked: drinkers filled, feed down, and a house or shelter standing open with dry bedding inside. Ducks released into a pen where water is already waiting go straight to it; ducks released into an empty pen mill about, call, and look for a way back to somewhere familiar.
Fill a shallow drinker they can dip their whole heads into, because ducks need to rinse their eyes and nostrils in water, and scatter a little feed near the house so the first exploration of the pen is rewarded. If the new property has resident ducks, keep the arrivals in a separate pen or a fenced-off section for the first days so introductions happen through wire rather than in a scuffle.
Release, count again, and watch the first hour
Carry the crates into the pen before opening them, set them down, and let the birds walk out in their own time rather than tipping them out. Count every bird out and match the number against the crate labels. Then step back and give the flock an hour of quiet: watch that they find the water, that no bird is sitting apart breathing hard, and that nobody is pacing the fence looking for an escape route.
Leave them shut in the pen for the first night rather than letting them range the new property straight away, so the pen registers as home. A KinsLe Care Pass lets whoever receives the flock at the new property see the headcount, the feeding routine and the pen layout for those first days, so nothing depends on a remembered phone call.