Preheat the oven to 200 degrees F. Place the avocado and lime juice in a medium bowl and toss to combine. Mix in remaining ingredients, except tortillas and salsa.
Heat two large non-stick skillets over medium heat. Place an equal amount of shrimp mixture on one half of each tortilla. Fold the tortillas over and gently press them down to create a half moon shape. Set one of the quesadillas in each skillet and cook 2 to 3 minutes per side, or until the cheese is melted and they are golden brown.
Set the quesadillas on a baking sheet and keep warm in the oven while you cook the other two. When ready to serve, cut the quesadillas into wedges and serve with the salsa.