Coat a baking sheet with cooking spray. Cut the sweet potatoes in half and scoop out into a medium bowl. Discard the skins. Smash with a potato masher or fork. Add flours, egg, cheese, salt and nutmeg. Mix well. Knead the dough until smooth (dough will be sticky). Set aside.
Boil water in a large saucepan. Divide the dough into 6 equal pieces on a lightly floured surface. Using the palms of your hands, roll the pieces of dough into ropes, keeping them at least an inch thick.
Cut the ropes into 1-inch thick pieces, about 8 per rope.
Place the dough pieces into the boiling water and cook until they float, about 2 to 4 minutes. Stir occasionally to prevent dough pieces from sticking together. Remove gnocchi with a slotted spoon or small strainer and place on the baking sheet. Repeat until all gnocchi are cooked.
Heat a large nonstick saute pan on medium-high heat. Add the oil. Saute the gnocchi until they are heated through and are light brown.