In a small bowl whisk the remoulade ingredients, including hot pepper sauce and pepper to taste. Cover and refrigerate until ready to serve or for up to 8 hours.
Shuck the oysters: Grip each oyster, flat side up, in a folded kitchen towel. Find the small opening between the shells near the hinge and pry it open with an oyster knife. Try not to spill the delicious juices, known as the “oyster liquor,” in the bottom shell. Cut the oyster meat loose from the top shell and then loosen the oyster from the bottom shell by running the oyster knife carefully under the body. Discard the top, flatter shell, keeping the oyster and juices in the bottom, deeper shell.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Grill the oysters, shell side down, over direct high heat, with the lid closed, until the edges of the oysters just begin to curl and the juices start to bubble, 2 to 4 minutes. Using tongs, carefully remove the oysters from the grill. Spoon about ½ teaspoon of the remoulade on top of each oyster. Serve immediately.