How to Make It
Place a jelly-roll pan in oven. Preheat oven to 450° (leave pan in oven).
Combine first 7 ingredients in a small bowl, stirring well. Chill until ready to use.
Combine okra and 2 tablespoons buttermilk; toss to coat. Sprinkle with 1/4 teaspoon salt; toss to coat.
Place shrimp in a medium bowl. Sprinkle with flour; toss well to coat. Drizzle with remaining 6 tablespoons buttermilk, and sprinkle with remaining 1/4 teaspoon salt; toss to coat. Drain okra and shrimp through a sieve; discard liquid.
Combine cornmeal and Cajun/Creole seasoning in a large zip-top plastic bag. Add okra and shrimp; seal bag, and shake well to coat.
Carefully remove pan from oven; drizzle with oil, tilting pan to spread oil. Remove shrimp and okra from cornmeal, shaking off excess; arrange in a single layer on pan. Bake at 450° for 5 minutes; carefully stir and turn over. Bake 4 minutes or until done.
Spread about 1 tablespoon rémoulade on one side of hot dog buns; divide lettuce and tomato evenly among buns. Divide shrimp mixture evenly among buns.