The short answer
Yes — zucchini is a safe, gentle vegetable.
Why
Zucchini (courgette) is soft, mild and hydrating, which makes it a great everyday veg and an easy one for nervous budgies to try. Skin and seeds are both fine.
How to feed it
Wash and offer a thin slice or small chunk, raw, with the skin on.
How much & how often
Can be offered daily as part of the fresh-food mix.