It's quite a site to see. Try it sometime. If the club doesn't have lights, other nearby clubs do. A loin cloth would do. There are no clothing rules.
Most shooters wear long-billed hats.
You'll get one very soon either from the club, a new friend, or manufacturer who sponsors trapshooting. Generally, just wear what you want. Shorts are fine. Bring sunglasses with you. Dress for the weather.