Make the yogurt sauce: Mix yogurt, sour cream, chipotles, and lime juice and zest in a small bowl. (Add more chipotle for a spicier sauce.)
Make the slaw: Mix mango, cabbage, avocado, and salt in a medium bowl. Toss with 1/4 cup yogurt sauce.
Make the shrimp burgers: Preheat oven to 425 degrees. Pulse a third of the shrimp in a food processor until a thick paste forms. Transfer to a bowl. Gently fold in egg white and remaining shrimp and yogurt sauce. Fold in breadcrumbs (mixture will be loose).
Scoop 1/2 cup shrimp mixture onto a baking sheet lined with a nonstick baking mat. Flatten into a 4-inch patty. Repeat. Bake until pink and firm, 8 to 10 minutes. Place 1 patty in each pita, top with slaw, and serve immediately.