Mix the paprika, brown sugar, chili powder and 1 teaspoon each cumin and salt in a small bowl.
Put the shrimp in a large resealable plastic bag. Add the juice of 1 lime, 1 tablespoon olive oil and the spice mixture; seal the bag and rub the spices into the shrimp. Refrigerate 30 minutes to 2 hours.
Meanwhile, heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the mushrooms and cook, stirring occasionally, until browned and tender, about 5 minutes. Add the corn, poblano, butter and the remaining 1/2 teaspoon cumin; season with salt. Cook, stirring occasionally, until the vegetables are lightly browned, about 3 minutes. Add the scallions and the juice of the remaining lime. Remove from the heat and cover to keep warm.
Preheat a grill to medium high and brush the grates with olive oil. Grill the shrimp until cooked through, about 2 minutes per side.
Warm the tortillas as the label directs. Serve the shrimp on the tortillas with the mushroom mixture; top with cheese. Serve with lime wedges.