In a medium bowl, combine mayonnaise, sour cream, and lime zest and juice. Add dill, Dijon mustard, and minced garlic. Season with salt and pepper. Whisk until smooth and creamy, then cover and chill.

Fill a pot with water and bring to a boil. Add shrimp and cook until pink and opaque, about 2-3 minutes. Remove from heat and prepare an ice water bath.

Transfer cooked shrimp to ice water bath to cool for about 3 minutes. Drain and chop shrimp into bite-sized pieces.

In a large mixing bowl, combine chilled shrimp, diced cucumber, and chopped green onions. Pour creamy dressing over and gently fold together.

Serve in a dish or plates, optionally on butter lettuce or in avocado halves.