Heat the oven to 375 degrees F. Spray 2 baking sheets with cooking spray.
Place the oats and nuts on a separate, unsprayed baking sheet and toast until golden, about 8 minutes. Set aside.
Combine the flour, baking soda, baking powder, salt, cinnamon, and ginger in a medium bowl.
Combine the egg whites, grated apple, applesauce, brown sugar substitute, white sugar, oil, and vanilla extract in a large bowl. Stir in the dry ingredients until just combined. Add the raisins and toasted oats and walnuts.
Drop the dough onto the prepared baking sheets by tablespoonfuls, about 2 inches apart.
Bake the cookies until golden, about 10 to 12 minutes.
Cool on wire racks for 3 minutes before removing them from the baking sheet. Cool cookies completely before serving. (These cookies can be made ahead and stored in an airtight container for up to 2 days.)