Heat oil in a saucepan (not more than half full) over medium-high heat to 365° on a deep-fat fry thermometer. Adjust temperature under pot to maintain 365°.
In a large bowl, whisk together the bread crumbs, Cajun seasoning and salt. Heat oven to 200°. Line a large baking sheet with a double layer of paper towels.
Toss 1/3 of the shrimp with egg whites. With tongs or a slotted spoon, transfer shrimp to bread crumb mixture and toss to coat. Fry in 365° oil for 2 minutes. Remove with a slotted spoon to papertowel- lined sheet and keep warm in 200° oven. Repeat twice more with remaining shrimp, egg whites and bread crumb mixture (you will have egg white and bread crumbs leftover).
Fry shrimp in 2 more batches, letting oil return to 360° to 365° before adding next batch.
Meanwhile, spread 1 tbsp tartar sauce on each hoagie roll or Italian bread section. Top each with 1/4 cup arugula leaves, about 8 shrimp and 2 tomato slices. Sandwich and serve.