The short answer

Yes — cucumber is a safe, hydrating vegetable and a good starter food for fussy budgies.

Why

Cucumber is mostly water, so it's light on nutrients but excellent for hydration, and its mild taste makes it a great way to introduce fresh food to a nervous bird. Skin and seeds are both fine.

How to feed it

Wash it and offer a thin slice or small chunk with the skin on.

How much & how often

Daily is fine, alongside more nutrient-dense vegetables.