Combine arugula, basil, corn and tomatoes in a large bowl. Whisk 3 tablespoons oil, lemon juice, vinegar, mustard and 1/4 teaspoon salt in a small bowl.
Sprinkle shrimp with the remaining 1/4 teaspoon salt. Heat the remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add the shrimp and cook, turning from time to time, just until they turn pink and are opaque in the center, about 3 minutes. Add to the arugula mixture along with croutons, if using.
Whisk the dressing again and drizzle over the salad; toss to coat. Divide the salad among 4 plates. Grind pepper over the salads and sprinkle with cheese.