grammaticality - Which Sunday do you prefer, if Sunday is OK with you?

Which Sunday do you prefer, if Sunday is OK with you?

Is the above sentence grammatically correct and natural? I'd like answers both from BrE and AmE speakers.

Sorry for my short, abrupt question. I do have my own opinion about this issue, but I'm remaining silent on purpose in order not to mislead you into saying things in favor of my potentially preconceived ideas.

By the way, I've asked the same question elsewhere as well. It's not that I don't trust the answerers there. It's just that the English learners around me may not trust me as a reliable source of information about the English language. I've been giving them my answer but they probably need confirmation from multiple sources.

Please note I'm not asking you to proofread the text. I wanted to ask you if the usage of the second "Sunday" is grammatically correct, idiomatic and natural. I was thinking that the usage of the second "Sunday" was wrong. It sounds unnatural. It is because, to me, it seems that if the speaker wants to ask whether there is any Sunday the other person is available, then (if he has to use this structure at all) he has to say "if a Sunday is OK with you" (with an indefinite article in it).

Thank you very much for your time.