Preheat air fryer to 350°. In a large bowl, combine mashed potatoes, cheeses, shallot, rosemary, sage, salt and pepper; stir in turkey. Shape into twelve 1-in.-thick patties.
In a shallow bowl, whisk egg and water. Place bread crumbs in another shallow bowl. Dip croquettes in egg mixture, then in bread crumbs, patting to help coating adhere.
In batches, place croquettes in a single layer in greased fryer basket; spritz with cooking spray. Cook until golden brown, 4-5 minutes. Turn; spritz with cooking spray. Cook until golden brown; 4-5 minutes. If desired, serve with sour cream.