For the shrimp marinade: Combine the mint leaves, rum, sugar, oil, lime pieces and 2 teaspoons salt in a medium bowl. Use a muddler or wooden spoon to mash, making sure to release the juices in the limes. Stir in the shrimp, then cover and refrigerate for 20 to 30 minutes.
For the taco cups: Preheat the oven to 350 degrees F.
Brush both sides of each wonton wrapper with oil, then press into the wells of a muffin tin, making sure to gently press into the bottoms and up the sides. Bake until lightly golden and crisp, 8 to 10 minutes. Remove the cups from the muffin tin immediately to a rack. Preheat the broiler.
For the mango avocado salsa: Stir to combine the mango, mint leaves, lime juice, red onion, rum and avocado in a medium bowl, then season with salt and pepper. Set aside.
Drain the shrimp from the marinade and place on a baking sheet. Broil the shrimp until cooked through, 2 to 3 minutes per side.
For the garnishes: Spoon the mango avocado salsa into the taco cups and top each with a shrimp. Garnish with chopped mint and queso fresco and serve with lime wedges.