Preheat the oven to 450 degrees F.
Rinse the salmon fillet and pat dry with paper towels. Cut the fish in half to make 2 fillets each about 4 by 4 1/2-inches in size. Starting on the longest edge, slice the fillets into 1/2-inch pieces.
Place the flour in a medium bowl and season with the salt and pepper. Place the egg whites in another bowl and beat until frothy, about 30 seconds. Combine the Parmesan and bread crumbs in a third bowl.
Coat the salmon pieces in the seasoned flour and pat to remove any excess flour. Dip the floured salmon in the egg whites and then into the Parmesan mixture, gently pressing the mixture into the fish. Place the breaded salmon pieces on a liberally oiled baking sheet. Drizzle lightly with the olive oil. Bake for 15 to 20 minutes until golden brown.
Mix the mayonnaise, yogurt, Dijon mustard, and parsley (or chives, if using) in a small dipping bowl.
Arrange the fish sticks on a serving platter and serve with the dipping sauce.