We haven't tested an egg-free version of this recipe, but we would start with some of the suggestions in this article on the best egg substitutes for meatballs. The purpose of the egg in this recipe is to serve as a binder: something that helps the meatballs hold their shape as they cook. You can also make something called a panade: add some milk to the bread crumb mixture and let it soak a bit before mixing it into the turkey meat, and it should have a similar effect.