The websites foolscap refers to, that would have you believe that “skin a cat” refers to a catfish, usually include some such remark as “Why on earth would anybody want to skin a real cat?”. People don’t realise, or just don’t like to believe, that there was a time when cat fur was much used for clothing and dead cats were routinely skinned, so routinely that there was a proverb “what can you have of a cat but her skin?” meaning, roughly, “you can’t get more, or different, value out of something than it intrinsically has”.
Here’s a nursery rhyme first printed as a broadside ballad in 1764 (from The Oxford Dictionary of Nursery Rhymes). The relevance to this thread is in the very last line so you don’t need to read the whole thing unless you feel like it!
There was a little man,
And he wooed a little maid,
And he said, “Little maid, will you wed, wed, wed?
I have little more to say,
Than will you, yea or nay?
For the least said is soonest mended, ded, ded.”
Then the little maid she said,
Little sir, you’ve little said,
To induce a little maid for to wed, wed, wed,
You must say a little more,
And produce a little ore,
Ere I to the church will be led, led, led.
Then the little man replied,
If you’ll be my little bride,
I will raise my love notes a little higher, higher, higher,
Though I little love to prate,
Yet you’ll find my heart is great,
With the little God of Love all on fire, fire, fire
The little maid replied,
“If I should be your bride,
Pray, what must we have for to eat, eat, eat?
Will the flames that you’re so rich in
Make a fire in the kitchen,
And the little God of Love turn the spit, spit, spit?”
Then the little man he sighed,
And some say a little cried,
And his little heart was big with sorrow, sorrow, sorrow,
I’ll be your little slave,
And if the little that I have,
Be too little, little dear, I will borrow, borrow, borrow.
Then the little man so gent,
Made the little maid relent,
And set her little soul a-thinking, king, king,
Though his little was but small,
Yet she had his little all,
And could have of a cat but her skin, skin, skin.