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A- Hi, Can I get this one, please? B- Sure. Anything else? A- No, that's it.

few minutes later ..

A- 1.Actually, Can you wrap it as a gift?

2.Do you mind if you wrap it as a gift?

3.Can you wrap it as a gift by any chance?

which one sounds natural?

or could you tell me if you know any better sentence?

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1 and 3 are both fine. "Actually" is appropriate here because it signals that you've changed your mind after your initial answer. 2 doesn't work, but you could change it to:

2* Would you mind wrapping it as a gift?

This would then be as good as the others. "Do you mind if..." fits when someone else is taking an action that affects the person you're asking, as in "Do you mind if I use your restroom?"

It's also more idiomatic to say "gift-wrap" instead of "wrap as a gift."

Under the circumstances you described I would most likely say a combination of 1 and 2*:

Actually, would you mind gift-wrapping it for me?

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