If you are willing to drive to Destin, Tightlines was excellent for fish sandwiches, and though we didn't have oysters there, others on the TripAdvisor forum have spoken highly of them for raw oysters. There is also Boathouse Oyster Bar, 288 Harbor Blvd, Destin, FL 32541, 850-837-3645 - we haven't been in a couple of years, but it was fabulous then.
Hurricane is open for lunch and located at 37 Logan Lane, ph 231.0787. They are a great choice for you.
I'd avoid the seafood at Shorty's but the fish is excellent. There is something about that grill that imparts an amazing flavor to every fish cooked on it.
Another choice for lunch might be Nick's on the Beach, 2210 West County Highway 30A Santa Rosa Beach, FL 32459, (850) 267-2117. Though I'd avoid the shrimp there, the fish sandwich was fabulous and we saw them serving raw oysters to a table at lunch (even though they aren't on the lunch menu) and we'd seen the huge bag of oysters come in just before that; it was handled by the owner, who seemed very expert with them.