In a medium bowl, combine the crab, softened cream cheese, celery, green onions, soy sauce, and Worcestershire sauce. Mix with a wooden spoon until fully blended.
Whisk the egg and water together in a small bowl to make an egg wash.
Lay an egg roll wrapper in a diamond shape with one corner facing you. Spoon 3 tablespoons of filling in a horizontal log across the center. Fold the bottom corner up over the filling, fold in both sides, then roll tightly toward the top corner. Brush the final corner with egg wash and press to seal. Repeat with the remaining wrappers.
Preheat the air fryer to 400°F for 3–5 minutes.
Brush all sides of each egg roll with egg wash, then spray lightly with cooking spray. Place in the basket in a single layer, leaving space between each one.
Air fry at 400°F for 8–10 minutes, flipping at the 4–5 minute mark, until deep golden brown and crisp. Work in batches if needed.
Rest for 2–3 minutes, then serve hot with sweet chili sauce.