I would make sure his bedding is changed a day or two before you move, so that you can keep that same bedding for a couple more days once you're in the new place. That way his cage will still smell somewhat like him, though the rest of his environment will have changed a bit. Other than that, make sure he has a familiar blanket in his carrier as well, make sure the temperature stays steady & safe, and try to keep him in a quiet area if you can, so he can still sleep. If you're moving a pretty decent distance, so that you'll have different water, it may also be helpful for him if you fill a couple of gallon jugs with your old water and switch him slowly to the new water - some hedgehogs are sensitive to a change in water. I haven't moved before, but these are all things I'd do if I were in the situation. Good luck with the move!