Prepare the spicy rémoulade: Stir together all spicy rémoulade ingredients in a small bowl. Cover and chill until ready to serve.
Prepare the Cajun pico: Toss together all Cajun pico ingredients in a medium bowl. Cover and chill until ready to serve.
Prepare the catfish: Stir together flour and 1 teaspoon each of the salt and black pepper in a shallow dish. Whisk together eggs and water in a second dish. Stir together cornmeal, 1 teaspoon of the salt, and remaining 1 teaspoon black pepper in a third dish. Sprinkle catfish with remaining 1/4 teaspoon salt. Dredge catfish strips, 4 at a time, in flour mixture, shaking off excess; dip in egg mixture, and dredge in cornmeal mixture, shaking off excess. Place on a wire rack in a rimmed baking sheet.
Pour oil into a Dutch oven, and heat to 350°F. Fry catfish strips, in batches, in hot oil until done, 4 to 5 minutes. Drain on a wire rack over paper towels. Place 2 catfish strips, 1 tablespoon of the rémoulade, and 1 1/2 tablespoons of the pico in each tortilla. Serve immediately.