Lightly spoon flours into dry measuring cups, and level with a knife. Combine flours and next 5 ingredients (flours through ground ginger); stir well with a whisk. Make a well in center of mixture. Combine 1 cup sugar, applesauce, and next 4 ingredients (applesauce through vanilla). Add to flour mixture, stirring just until moist; cover and chill dough at least 1 hour.
Preheat oven to 350°.
Lightly coat hands with flour. Shape dough into 24 balls (about 2 tablespoons each; dough will be sticky). Roll balls in 1/4 cup sugar. Place balls 2 inches apart on baking sheets coated with cooking spray. Bake at 350° for 15 minutes or until lightly browned. Cool 1 minute on pan. Remove from pan; cool completely on wire racks.
Note: These freeze well. Place cooled cookies in a heavy-duty zip-top plastic bag; store in freezer for up to 1 month. Thaw at room temperature.