Make the Key lime aioli: In a small bowl, whisk together the mayonnaise, lime juice, salt, and hot sauce until well combined, then refrigerate until ready to serve.
Make the fritters: Fill a medium pot with 4 inches of vegetable oil and heat over medium heat until the temperature reaches 350°F (180°C).
Add the conch meat to a food processor and pulse until finely minced. Scoop the conch into a large bowl and wipe the food processor clean.
Add the carrot, celery, jalapeño, bell pepper, red onion, and cilantro to the food processor and pulse until finely chopped, leaving some larger pieces for added texture.
Transfer the mixture to the bowl with the minced conch, along with the flour, curry powder, baking powder, cayenne, salt, and beer. Stir until just combined, being sure not to overmix.
Working in batches of 8–10 at a time, use a 1-ounce scoop to portion the batter into the hot oil and fry, turning the fritters frequently with a slotted spoon or spider, until crispy and golden brown, about 4 minutes. Transfer to a rack lined with paper towels to drain and repeat with the rest of the batter, letting the oil return to temperature between batches.
Serve the fritters warm with the lemon wedges and Key lime aioli.