I can tell you that moving is stressful for cats too! We moved over the summer and our two (which have grown up together and are best buds) would swat at each other. I think cats can sense stress! They're also not happy when furniture gets moved and things get put in boxes.
I would say to introduce them to the new place slowly. They will both get used to it on their own terms. Our first day in the new place, Pandora was under the bed and Thor was checking out every nook and cranny. I've heard people talk about using a diffuser called Feliway which helps keep cats calm during a big transition like this. It seems to work well for our cats, some people don't see a difference but it might be worth a try if your kitties are on edge.
You might be able to find an inexpensive, small scratching post at a place like Petsmart. They seem to have all different shapes and sizes.