Make the remoulade: Stir together all ingredients; refrigerate for 20 minutes.
Meanwhile, preheat oven to 400 degrees. Make the oysters: Bake cornmeal on a rimmed baking sheet, stirring halfway through, until pale gold, 10 to 12 minutes. (It may begin to smoke.) Let cool. Transfer to a bowl; stir in cayenne.
Heat baking sheet on lower rack of oven for 5 minutes. Meanwhile, whisk whites until frothy but still loose, 1 to 1 1/2 minutes. Add oysters, and mix to coat completely. Dredge each oyster in cornmeal mixture, shaking off any excess; transfer to a plate. (You should use only about 1/2 cup cornmeal.) Generously coat oysters with cooking spray.
Line warmed baking sheet with parchment. Transfer oysters, sprayed side down, to sheet. Coat generously with cooking spray. Bake until cooked through and just turning golden brown, 7 to 8 minutes; transfer to a plate.
Preheat broiler with rack in top position. Toast buns, split side up, until golden brown, about 1 minute. Divide remoulade evenly among bun halves. Sandwich oysters and lettuce between buns. Serve warm.