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A young missionary travels to Senegal to teach God's way to a local tribe.

Upon reaching the village, he is not well received by the inhabitants, but he slowly and steadily create contact. After many years he's finally accepted by the people and goes along well with everyone, until one day the chief's daughter gives birth to a white child.

Infuriated but not ungrateful for what the missionary has done for the village, he gives him one chance to explain himself in private.

The young man, who is innocent, tells him "I have nothing to do with it, it is just a hazard of the genetics. It's the same as with sheeps, most of them are white but sometimes a black one is born for no reason".

The chief steps back a little, gives a frightened look to the missionary, then whispers : "Ok, I won't say a word about my daugther, but don't you tell anyone about the sheep"

Leaving aside the origins of this rhyme and various controversies surrounding it, the formation "have you any wool?" is interesting. One would expect (1) "Do you have any wool?" or (2) "Have you got any wool?". I personally use the formation in (2) more but I think (1) is the more common one. You can read more in the answers to this this SE question: https://ell.stackexchange.com/questions/101667/use-of-have-i...
Looking at your link this may not be the original cause, but I always thought the purpose was to make it correctly fit the meter (sung to the tune of "Twinkle Twinkle Little Star" - or the tune of the alphabet song). "Do you have" or "Have you got" are both one syllable too long.
I think it was standard English when the rhyme was made.

I perceive it as more polite than "have you got" or "do you have".

(Native English English speaker.)

As a native non-English English speaker, I can see that. (Thinking it in an English accent helps.)
Also, for black sheep, see "Judas sheep".[1] Black sheep were sometimes trained to lead the other sheep to slaughter.

[1] https://wordhistories.net/2019/08/30/judas-sheep-judas-goat/

the article there doesn't seem to mention black sheep?
I recall that the "“But none for the little boy who cries in the lane.” was the form I heard as a child and I wasn't alive in the mid-eighteenth century...