Combine broth, 1 tablespoon lime juice, and oregano in a large saucepan; bring to a simmer. Cook 5 minutes. Discard oregano. Add shrimp to pan; cook 3 minutes or until done.
Transfer shrimp mixture to a large bowl. Stir in ice, tomato juice, and hot sauce. Let stand 1 minute or until ice melts. Stir in remaining 1/4 cup lime juice, onion, tomato, cucumber, pepper, and salt. Cool. Cover and chill.
Stir in cilantro. Divide shrimp mixture evenly among 6 bowls; top with avocado. Garnish with lime wedges.
Wine note: One wine has a lot to match in this bold shrimp cocktail. Lime, tomato, hot sauce, shrimp, avocado--they all impact wine differently. With so many elements at play, serve a simple, dry, refreshing white that's flexible with all sorts of seafood. One of the best is albariño, the snappy, stylish white from Spain. Try Nora Albariño 2005 from Rias Baixas, Spain ($15). --Karen MacNeil