I don't think there's a restriction on what they eat, just what they will or won't eat. Favorites of my BNs are zucchini and canned green beans. I used to feed cucumbers but don't anymore because zucchinis are suppose to be more nutritious.
You can freeze your zucchini. I slice up a fresh zucchini into slices and just stick them in the freezer. When you need to feed just take what you need and let the rest stay in the freezer. Might not be fresh but mine don't seem to complain