Pat peeled and deveined shrimp dry with paper towels. Sprinkle with chile powder and salt, slightly rub in.
Heat olive oil in medium skillet over medium-high heat. Add shrimp and cook for 5 to 6 minutes, stirring. Shrimp will be done when they have turned pink and are no longer translucent. Take care not to overcook. Transfer shrimp to plat to cool for 5 minutes.
Meanwhile, slice persimmons and avocado and arrange on plate. Sprinkle with feta and cilantro and top with cooled shrimp.
To make lime vinaigrette, add all ingredients for dressing into small jar and shake until emulsified.