Blend mayonnaise, scallions, pickle, capers, hot sauce and 1 tsp. Cajun seasoning in food processor. Cover and chill.
Whisk egg, milk and cayenne.
Add shrimp; let stand 10 minutes. In a shallow bowl, mix cornmeal, flour, 1 Tbsp. Cajun seasoning, salt and pepper. Preheat oven to 200F; line a baking sheet with paper towels and another with foil.
Remove shrimp from egg mixture, shaking off excess. Dredge in cornmeal mixture. Set on foil-lined sheet.
Pour 2 inches of oil into a large, deep skillet.
Heat oil until it reaches 370F on a candy thermometer. Cook shrimp a few at a time, turning once, until coating is browned and crispy, 3 to 4 minutes.
Remove to paper towel-lined sheet with a slotted spoon. Keep warm in oven. Bring oil back to 370F before adding a new batch of shrimp.
Spread 1 Tbsp. reserved sauce on rolls. Divide lettuce and tomatoes among rolls. Divide shrimp among rolls and serve immediately.