Combine the cucumber, radishes, shallot, vinegar, 1 tablespoon of the oil, and ½ teaspoon each salt and pepper in a medium bowl.
Combine the cornmeal, Cajun seasoning, and ¼ teaspoon salt in a shallow bowl. Dip the tilapia in the cornmeal mixture, pressing gently to help it adhere.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat. Add the tilapia and cook until opaque throughout, 3 to 4 minutes per side. Let cool slightly, then break into pieces.
In a separate medium bowl, gently toss the tilapia with the celery, celery leaves, and the remaining tablespoon of oil.
Spread the buns with the mayonnaise and fill with the tilapia salad, dividing evenly. Serve with the radish and cucumber salad.