To me the precise procedure will depend some on what the new coop and run look like and if the old coop shares the same run. But those are mostly just details.
My general procedure for older ones is to move them from the old to the new after dark. They are easier to catch after dark. They may freak out some but it's probably less than doing it during the day. They will get over it. They will not suffer any long term psychological damage either way. They will be OK, sounds like it will bother you more than it will them.
My grow-out coop shares a run with the main coop. When they wake up the nest morning I open the pop door and leave them on their own. I close the old coop so they cannot go back in there. Sometimes they put themselves to bed in the new coop the next night, sometimes they try to go back to the old coop. If they do I wait until after dark and they are easy to catch and lock them in the new coop overnight. It usually doesn't take them long to make the switch themselves.
When I move the chicks from my brooder to my grow-out coop I do that during the day. They are easy to catch in the brooder. I often leave them locked in the grow-out coop only for a week before I let them out into a section of run that is isolated from my main run. When I let them into that run section they often want to sleep in the run instead of putting themselves to bed in my grow-out coop. So I go out after dark when they are easy to catch and lock them in the coop section overnight. They may get that message pretty quickly or it may take a while before they put themselves to bed on their own. But if you are consistent. they will.
I'm different to you in that I have mature chickens in the main coop and run. That affects some of my details. But the general procedure is the same. Move them when it is most convenient to you and consistently put them to bed where you want them to sleep.
My general procedure for older ones is to move them from the old to the new after dark. They are easier to catch after dark. They may freak out some but it's probably less than doing it during the day. They will get over it. They will not suffer any long term psychological damage either way. They will be OK, sounds like it will bother you more than it will them.
My grow-out coop shares a run with the main coop. When they wake up the nest morning I open the pop door and leave them on their own. I close the old coop so they cannot go back in there. Sometimes they put themselves to bed in the new coop the next night, sometimes they try to go back to the old coop. If they do I wait until after dark and they are easy to catch and lock them in the new coop overnight. It usually doesn't take them long to make the switch themselves.
When I move the chicks from my brooder to my grow-out coop I do that during the day. They are easy to catch in the brooder. I often leave them locked in the grow-out coop only for a week before I let them out into a section of run that is isolated from my main run. When I let them into that run section they often want to sleep in the run instead of putting themselves to bed in my grow-out coop. So I go out after dark when they are easy to catch and lock them in the coop section overnight. They may get that message pretty quickly or it may take a while before they put themselves to bed on their own. But if you are consistent. they will.
I'm different to you in that I have mature chickens in the main coop and run. That affects some of my details. But the general procedure is the same. Move them when it is most convenient to you and consistently put them to bed where you want them to sleep.