When I moved my birds to Neuchickenstein I moved them out of 3 small coops after it was fully dark -- carrying them down and settling them on the perches of the new coops.
It was a bit of a production number (4 people with multiple pet carriers, etc.), but I stayed in the coop with a dim, red headlamp on until I was sure they were settled.
My general philosophy is that chickens are tough, adaptable animals who can adjust reasonably well to different situations as long as I provide the basics and act calmly myself so that they don't pick up on external stress.