If being taken as rude is a concern, you can make the question more polite by adding -ㄴ/는지 여쭤봐도 될까요?
- 언제 제 상품을 배송해 주실 수 있나요? (normal question)
- 언제 제 상품을 배송해 주실 수 있는지 여쭤봐도 될까요? (May I ask ...; Would you mind if I ask when you'd be able to ..).
(Also, if it's not a commercial product, you could say 아이템 instead of 상품)
- 언제 되나요? (When can it be done?)
- 언제 되는지 여쭤봐도 될까요? (Would you mind when it can be done?)
- 언제 보내주실 건가요? (When are you going to send it to me?)
- 언제 보내주실 건지 여쭤봐도 될까요? (Would you mind my asking when you're going to send it to me?)
This expression is almost too polite, so it's not a good idea to overuse it.