Mix the mayonnaise, 1/4 cup hot sauce, the mustard, pickle, shallot and parsley in a small bowl; cover and refrigerate.
Preheat the oven to 250 degrees F. Heat 2 inches of peanut oil in a large wide pot over medium-high heat until a deep-fry thermometer registers 365 degrees F.
Meanwhile, whisk the flour, beer and the remaining 3 tablespoons hot sauce in a large bowl; add the shrimp and toss to coat. Working in batches, remove the shrimp from the batter with a slotted spoon and fry until cooked through and golden brown, 2 to 3 minutes. (Return the oil to 365 degrees F between batches.) Transfer to a paper towel-lined baking sheet to drain; keep warm in the oven.
Add the celery to the remaining batter and toss to coat; remove with a slotted spoon and fry until golden brown, about 2 minutes. Serve the fried shrimp and celery with the prepared sauce.