Combine first 5 ingredients in a small bowl, stirring with a whisk. Gradually add oil, stirring constantly with a whisk.
Bake tortilla shells at 350° according to package directions.
While shells bake, heat a grill pan over medium-high heat. Combine shrimp, chili powders, and salt in a large bowl; toss well to coat. Coat pan with cooking spray. Add shrimp to pan; cook 2 minutes on each side or until done.
Combine lettuce, mango, tomato, and radishes. Drizzle vinaigrette over salad; toss to coat. Place about 1 1/2 cups salad in each tortilla shell; divide shrimp evenly among salads.