Preheat the oven to 375°F (190°C). Lightly grease a baking dish with cooking spray.
Place each chicken breast between two sheets of plastic wrap and gently pound with a meat mallet or rolling pin until about 1/4 inch thick.
Remove the top plastic wrap. On each flattened chicken breast, layer one slice of low-fat ham and one slice of low-fat Swiss cheese.
Roll up each chicken breast tightly, tucking in the sides to enclose the filling. Secure with toothpicks if necessary.
In a shallow bowl, whisk together the egg whites and water until combined.
In another shallow bowl, combine whole wheat breadcrumbs, grated Parmesan cheese, garlic powder, dried Italian seasoning, salt, and black pepper.
Dip each chicken roll into the egg white mixture, allowing excess to drip off, then coat thoroughly with the breadcrumb mixture.
Place the coated chicken rolls seam side down in the prepared baking dish. Lightly spray the tops with cooking spray.
Bake in the preheated oven for 25 minutes, or until the chicken is cooked through (internal temperature reaches 165°F/74°C) and the coating is golden brown.
Remove toothpicks before serving. Let rest for 5 minutes before slicing and serving.