1. Whisk together first 8 ingredients in a small bowl; cover and chill.
2. Place eggs in a single layer in a stainless-steel Dutch oven. (Do not use nonstick.) Add water to depth of 3 inches. Bring to a rolling boil; cover, remove from heat; let stand 15 minutes.
3. Drain immediately, and return eggs to Dutch oven. Fill Dutch oven with cold water and ice. Tap each egg firmly on the counter until cracks form all over the shell. Peel under cold water.
4. Slice eggs in half lengthwise, and carefully remove yolks, keeping egg white halves intact. Mash yolks with mayonnaise mixture until smooth using a fork; stir in shrimp. Spoon yolk mixture into egg whites. Serve immediately, or cover and chill up to 24 hours.