You are moving not far away, right?

What I have done when I have moved short distances is move my cats last. I keep them in the room that holds their litter boxes/food while the actual moving is going on so they don't sneak out. This has not been a big problem for me in the past - most of my cats hide when strange people (people helping me move) are over.

I usually try and get a bunch of strong men to help me move, that way I can supervise and keep an eye out for the cats and make sure no one enters that room.

Then when all the familiar stuff is in the new place, the cats are loaded in the carrier, litter box and food dishes are packed, then all moved together. I don't start putting little stuff away until the cats are mostly settled in. This can take a few days. I think they feel better going to a new place with all the old stuff there already.