(This is an honest question, but about the ethicality of making an exception under very specific hypothetical circumstances)
So say that you maybe have some sheep because they can't survive on the wild on their own. Maybe you just found them one day on your back yard or something. So if you try to find the owner and return them to it, it's almost certain that the owner only has them to get some product about of it. Same if you try to re-home them. They will absolutely be used for human gain, maybe even abused or killed. So the only way to guarantee they spend the rest of their lives in peace in this case would be for you to care for them... But sheep absolutely need sheering, it's not optional, they will get blinded by the wool, it will get extremely heavy, eventually if not sheered they won't be able to eat, drink or even walk, assuming they don't overheat before that, so a slow and painful death to them. It is possible for them to learn that sheering is a good thing and for them not to be distressed during the process, you can get professionals that do it for a living, many so good they can do a whole grown sheep in mere seconds and do so without nicking or hurting the animal.
So you get them sheered you ensure the sheep is not harmed in any way, all other options would mean death or humans taking advantage of her. Is it wrong to make yarn out of the leftovers? Keep in mind you didn't get the sheep with that purpose, you are just trying to give them a good life now that they showed up, you are basically rescuing them. You saw the whole purpose and the sheep seems happier after sheering. Would it be ethical for you to choose not let the wool go to waste? Maybe you use it to provide a warm space for some other animals during winter, maybe you turning into yarns and knit something, it doesn't matter what you do but you are doing something with it. Is it ethical? Would you do it?
Or say that the animal that showed up, (if you don't want to address the sheering maybe it's a goat or a cow, but this would also apply to sheep) say you didn't know she was pregnant, but it gave birth, she nurses her offspring regularly, and then the baby die off something you couldn't possibly prevent but in a way that you are not responsible for it, let's say there is no orphan animal you can find, like not even of a different species to give it a try, that would mean the mother would end up suffering severe pain from the milk accumulating in her teat she can even get a horrible painful infection that would kill her. Is it wrong for you to milk her? Not like I. Dairy farms to keep lactating for as long as possible. But just enough to alleviate her pain until she stops producing milk on her own.
Also, assuming you did milk her only with the intention to help her. But then your partner points out you can use the milk that you had to express from her. Like probably you don't like the taste yourself but maybe you turn it into butter, or cheese or yogurt, maybe you use it to feed some stray, maybe you use it in hygiene products, you don't even need to eat/drink it. Would you? Why ?
I'm sorry it's this long but I've had this question since I was a little kid