Mix the butter, garlic and 1/2 teaspoon salt in a small bowl. Spread 2 tablespoons of the garlic butter on the flat outsides of each bun. Heat a large nonstick skillet over medium heat. Add the buns and toast until golden brown, about 3 minutes per side. Remove to a plate and wipe out the skillet.
Heat 1 tablespoon olive oil in the skillet over medium-high heat. Add half of the shrimp in a single layer and season with salt. Cook until lightly colored on the bottoms, about 45 seconds. Add 1 tablespoon of the garlic butter and cook, tossing, until the shrimp are coated but not fully cooked, 20 to 30 seconds. Transfer to a plate along with any juices from the pan. Wipe out the skillet and repeat with the remaining 1 tablespoon olive oil, shrimp and 1 tablespoon garlic butter.
Add the wine, lemon zest and juice and red pepper flakes to the skillet; carefully pour in any juices from the plate of shrimp. Cook over medium-high heat until reduced to about 1 tablespoon, 1 to 2 minutes. Return the shrimp to the skillet and cook, stirring, until cooked through, 15 to 30 seconds. Remove from the heat and stir in the remaining garlic butter and parsley. Season with salt.
Line each hot dog bun with lettuce leaves and fill with the shrimp; drizzle with some of the pan juices. Serve with lemon wedges.