1. Finely slice lettuce to make about 8 cups. Coarsely shred cucumber and radishes.
2. In medium-sized bowl, mix mayonnaise and next 6 ingredients until blended and smooth. Add sliced lettuce, shredded cucumber, and radishes; with rubber spatula, toss ingredients to coat with dressing. Cover and refrigerate slaw while preparing fish.
3. Separate fish into fillets. If fillets are large, cut each crosswise in half. In pie plate, beat egg. Onto waxed paper, measure bread crumbs. Dip fish in egg, then into bread crumbs, pressing crumbs onto fish to coat.
4. In 12-inch skillet over medium heat, in hot salad oil, cook fish, a few pieces at a time, about 5 minutes or until fish flakes easily when tested with a fork, turning fish once and removing pieces to warm platter as they brown.