Our cats are very very shy and we really worried about how to make our recent house move smooth. In the end we shut them in the bathroom while the house was being packed and loaded, left them in there overnight, then on move day took them to the local vet for day boarding while the actual move/unloading happened. Then we collected them and took them back to the new house.
They hated the whole business but it worked out OK, because they were due a vet checkup anyway. But if I had to do it again I'd probably just check them in for 1-2 nights at a cattery. I hate putting cats in a cattery but ultimately it's probably the least distressing option as the way we did it meant they were shut in the bathroom listening to strangers thumping about and stuff being moved all day and were really frightened and upset.
Also if you haven't already buy some Feliway spray for when you move. We found spraying it on the room where we kept them at first really made a difference to how quickly they relaxed into their new home.