Cut the cooked shrimp into small bite-size pieces and transfer to a bowl. Add the mayonnaise, red onion, diced cucumber, lime zest, lime juice, and salt. Mix gently until well combined. Set aside.
In a blender or food processor, combine the avocado, cream cheese, lime juice, olive oil, and salt. Blend until completely smooth and creamy, scraping down the sides as needed.
Place a 6-inch ring mold on a serving plate. Spoon the shrimp mixture into the mold, pressing lightly to create an even layer. Avoid adding excess liquid released from the cucumber.
Spread the avocado cream evenly over the shrimp layer and smooth the top.
Carefully remove the ring mold. Garnish with extra shrimp and chopped chives if desired.
Serve immediately or refrigerate until ready to serve.