In a small bowl, mix together the mayonnaise, key lime juice, salt, and hot sauce until smooth. Place in the refrigerator until ready to use.
For the Fritters:
Fill a medium pot with about 4 inches of vegetable oil and heat over medium until the oil reaches 350°F.
Using a food processor, finely mince the conch meat, then transfer it to a large mixing bowl. Clean the processor bowl, and then add the carrot, celery, jalapeño, bell pepper, red onion, and cilantro. Pulse the vegetables until finely chopped, leaving some slightly larger pieces for texture. Add this mixture to the conch in the bowl.
Next, sift together the flour, baking powder, curry powder, cayenne pepper, and kosher salt. Add this dry mix to the conch and vegetables. Slowly pour in the beer while stirring, mixing until just combined. Avoid overmixing to keep the fritters light.
Working in batches, use a 1-ounce scoop to drop the batter into the hot oil. Fry the fritters, turning them frequently, until they are golden brown and crispy, about 4 minutes. Use a slotted spoon to transfer the fritters to a rack lined with paper towels to drain. Let the oil return to temperature before starting the next batch.
Serve the fritters warm with lemon wedges and the chilled Key Lime Aioli on the side.