Combine the curry powder, cayenne, 2 teaspoons salt and 1 teaspoon black pepper in a bowl. Combine the chicken, half of the spice mixture, the yogurt, 1 cup milk and the garlic in a large resealable bag; shake to coat. Refrigerate at least 2 hours or overnight.
Preheat the oven to 350 degrees F. Spread 1/2 cup coconut on a baking sheet and toast, stirring occasionally, until golden, about 12 minutes; transfer to a medium bowl and set aside. Combine the remaining 1/2 cup coconut, the flour and the remaining spice mixture in a large bowl; work in the remaining 1/3 cup milk with your fingers until small lumps form.
Set a wire rack on a baking sheet. Heat about 4 inches of equal parts peanut oil and shortening in a large pot over medium-high heat until a deep-fry thermometer registers 350 degrees F.
Remove the drumsticks from the marinade, letting the excess drip off. Using your hands, coat the chicken with the flour mixture, pressing it so it sticks to the meat. Place on a plate.
Working in 2 batches, carefully add the chicken to the hot oil mixture. (The temperature will drop to 300 degrees F to 325 degrees F; adjust the heat to maintain this lower temperature.) Fry, undisturbed, 2 to 3 minutes to set the crust. Continue frying, turning as needed, until golden brown and cooked through, 10 to 12 minutes. Remove to the rack; sprinkle with salt, transfer to the oven and bake until a thermometer inserted into the thickest part registers 165 degrees F, 10 to 15 minutes.
Meanwhile, add the red onion, mango, cilantro, lime juice and a pinch of salt to the toasted coconut. Sprinkle the mixture on the chicken.