Combine first 9 ingredients in a medium skillet over medium-high heat. Bring to a boil; reduce heat and simmer 15 minutes or until thick. Set mango chutney aside.
Heat 2 teaspoons oil in a large skillet over medium-high heat. Place 4 crabs in pan, top sides down; cook 2 minutes per side, gently pressing body and legs against pan. Place sautéed crabs, top sides up, on a baking sheet. Repeat procedure with remaining oil and crabs.
Combine coconut, mustard seeds, salt, and egg white; divide evenly among top shells of crabs. Press coconut mixture on top shells of crabs, leaving a 1/8-inch margin around outside edge of shells. Lightly spray crabs with cooking spray. Place baking sheet 8 inches away from broiler; broil 5 minutes or until coconut mixture is browned and crisp.