I know I need to be appear confident, but I'm sure my nervousness shows. Is there anything I can do?

Rehearse. Consider asking a friend who is familiar with your work to sit down and ask you questions like an construction interviewer. Dress the part. Set up the rehearsal space as much like the construction interview space as possible. If you can, video the rehearsal. If you can't video, ask your friend to pay attention to your body language. When you review the tape or discuss the experience with your friend, you may discover that you come off just fine. You may also discover that you have nervous habits or mannerism that you can work on.