There's more than one way to skin a cat.
The whole nine yards.
Also, there was a thread where a lot of foreigner CS students use english words because many of the words don't have direct translations or sensible translations - like mouse.
"There are multiple valid solutions for a given problem"
Skinning a cat is not a common thing. It’s not a normal food for English speakers, so the phrase carries some sense that what you’re doing is unusual.
It’s usually applied to a situation completely unrelated to skinning or otherwise preparing food, so it carries some sense of absurdity.
Most people using the phrase have never skinned anything, so there’s (usually!) a sense of ignorance on both sides.
Your translation brings none of that.
If I were to translate that idiom back to English and aim for accuracy, it would be something like, “what you’re doing is unusual, and neither of us have experience doing it, and the way you’re doing it is different than the ways I have heard of, but I suppose there’s more than one valid way to do it.” Which, I think, fits the spirit of the other examples - a very short expression that carries tons of unspoken cultural context with it, to the point that there isn’t a direct translation.
"There are multiple valid solutions for a given problem"
This Economist article[1] posits that it is actually slang for sexual intercourse based on the phrase "skin the cat"[2] first recorded in 1837 being a euphemism for it. This interpretation would also fit with the above quote. The same article also points out that:
'And the rather violent act of skinning a cat is no easy thing, says John Youngaitis, a taxidermist in New York. “There is not more than one way to skin a cat.”'
From[0] we can also see that in 1678 English naturalist John Ray said in his “Collection of English Proverbs”: “There are more ways to kill a dog than hanging”.
So it seems it is possible that the contemporary phrase exists to change a less common activity for a more common one. In this case use of the idiom would not convey the sense of doing something unusual.
[0] https://www.bnd.com/living/liv-columns-blogs/answer-man/arti...
[1] https://www.economist.com/prospero/2013/10/09/shooting-skinn...
Many proverbs in different languages have a common meaning but a different way to "deliver" it, I always find amusing how a differnt language/culture gets to the same point with completely different means.