Hey, Congrats on your new babies! I've found the best way to travel with a new critter is to basically keep him in a warm dark cardboard box with a towel. You don't want a box too big so he slides around in it, nor do you want a box that will cramp him. As long as he feels warm and in the dark, he should feel safe. Cardboard "breathes", so should be fine for an hour's car ride.
when you go to open the box, make some noise, talk to him, let him know whats going to happen, that you're going to take him out, then open the lid carefully/slowly. I find that talking to them before/as you approach helps them to know you're not going to hurt them, especially after the trauma of traveling.
I use this technique for traveling to and from the vet, and it has worked great. Even if your skink doesn't understand English, I think they understand body language/voice tone enough to recognize that no harm is meant for them. Communication is good for every species, we just need to learn their language!

Good luck! Hope this helps!
Saille