Toss the shredded cabbage with ½ teaspoon salt. Place in a colander and let stand 15 minutes. Wrap in a clean kitchen towel and squeeze out as much liquid as possible.
In a large bowl, combine the squeezed cabbage, shredded chicken, cilantro, jalapeño, cranberries, mayonnaise, rice wine vinegar, sugar, and black pepper. Mix until evenly combined.
Place a wrapper in a diamond orientation. Spoon a scant ¼ cup of filling into the lower third, shaping it into a 4-inch log.
Brush all edges with egg wash. Fold the bottom corner up and tuck under the filling, fold in both sides, then roll upward tightly and press to seal. Set seam-side down. Repeat with remaining wrappers, keeping finished rolls covered.
Preheat the air fryer to 375°F for 3 minutes.
Spray the basket. Arrange the egg rolls seam-side down in a single layer without touching. Spray the tops generously.
Cook at 375°F for 8 to 10 minutes, flipping and re-spraying at 5 minutes, until deeply golden and crisp. Work in batches.
While they cook, blend all dipping sauce ingredients until smooth.
Rest the egg rolls 2 to 3 minutes before serving with the cilantro lime sauce.