I see you are a bit more worried about the girl cat (obviously). On the move day, I’d suggest you let the cats occupy a room that you’ve already vacated.
Add in all their favourite toys in the mover to keep them engaged and ensure that you block out all the clangs and bangs that are bound to emanate from all the moving around. On the moving day, make sure that you inform the movers about your confident tom and your nervous girl and to be super cautious when moving stuff around. Put up a board or something for good measure. During the commute to your new place, I’d suggest that you accompany your cats separately in another vehicle so that they know they are with someone whom they trust minus the clanging and banging.
Once you are done moving, expose the new place slowly and gradually to your cats. Let them investigate the place on their own and take the new place in. Make use of items from your old place so that they recognise the familiar smells which will make them feel secure. This will surely help your cats bond with the new place. Keep the mover in a specific spot though and be sure that it is the exact place where you will want to locate your cats. Accompany your cats when they are roaming around the house and keep an eye on them to see if it is calm or is anxious. And soon enough, your both your cats will get used to the new home.