Can you really substitute for an egg? Wouldn't that be the levening agent? I'd say hoof it to the store.

Do you have neighbors ;)?

You're joking, right? Chocolate chip cookies from a mix? You're not joking? Sub 1/3 cup applesauce, mayo or Miracle Whip, or some flax seed mixed with water. Or skip it completely and add 1/4 cup extra water.

The replacement for 2 eggs is (according to adventuresofaglutenfreemom.com): 4 tablespoons water + 2 tablespoon oil + 1 teaspoon baking powder, beaten together until smooth. If you don't have oil, I'd try melted butter in place of the oil.