Preheat oven to 350°. Coat a 6-cup mini Bundt pan with spray.
Combine flours, sugar, baking powder, baking soda, salt, and nutmeg in a large bowl. Whisk egg, egg white, yogurt, and oil in a separate bowl.
Add wet ingredients to dry ingredients, stirring until just blended. Fold zucchini and figs into batter. Pour batter into pan.
Bake until a wooden skewer or toothpick inserted into the center of a cake comes out with a few moist crumbs attached (40 to 45 minutes). Let cool 5 minutes, then transfer to a wire rack to cool completely. Dust with powdered sugar, if desired.