Not Veterinary Advice: Yes, you can feed your iguana cucumber. It doesn't have a lot of nutrients, but okay on occasion for additional water and flavor.
Green iguanas originate from the rain forests of northern Mexico to southeastern Brazil where the temperatures and humidity are high. Iguanas live in the trees and bask in the sun. They eat only vegetation: up to 50 different kinds of leaves, flowers, and fruits.
All plant material should be washed, chopped (a food processor is recommended), and thoroughly mixed. Chopping and mixing will ensure a balanced diet because the iguana will eat all the food items and not be able to just pick out the favorite or tasty ones.
The table below shows some food items that you can feed your iguana.
Green Iguana Basics: Diet, Housing, and Cleaning via kwout
You can find more information on iguana care at the following sites:
Green Iguana Society
PetPlace
peteducation.com
Learn the secret tips to adopting an iguana at Resource for Iguana Care and Adoption.