Line a baking sheet with paper towels; set aside. Combine flour, salt, and pepper in a large shallow dish. Dredge crabs in seasoned flour, tapping off excess; set aside.
Heat a large skillet over medium-high heat. Add butter and oil to skillet. When butter has melted, add crabs and cook until deep golden brown, about 4 minutes per side. Transfer crabs to a prepared baking sheet to drain. Sprinkle with salt. Serve immediately with lemon wedges.