I don't completely understand your question, but I guess this could help you.
خِیر in Farsi means "No", as you pronounced it. خَيْر simply means "goodness" in Arabic but in Farsi is common to pronounce خِیر with this meaning!
Under the Persian Etymology 2 section, it’s stated to be a “Clipping of نه خیر (na xeyr)”. You seem to have mistakenly looked at the etymology of Urdu خیر which is stated to be "From Arabic خَيْر (ḵayr), possibly via Persian خیر (xayr)".
Many thanks desi4life for taking time on this, I am however sure I am missing a trick here, is the answer staring me in the face but I can't see it?
Etymology 1: I know خیر/xeyr means "good" in Arabic & I am desperately hoping that this is not the same خیر/xeyr in نه خیر.
Etymology 2 I can see that it says خیر is a 'Clipping of نه خیر', but where does it say what خیر itself means? It is obvious the key part of نه خیر in نه/nah "no" so what does خیر mean here, what does it add, is it used in other words?
Also isn't "Clipping of نه خیر" a different way of saying "we don't know"?