A problem generally has more than one solution. Or, there are always several ways to accomplish the same goal.
In 1855, Charles Kingsley used one old British form in Westward Ho!. “There are more ways of killing a cat than choking it with cream.” Or, “choking it with butter.” For a dog, it was said, “there are more ways of killing a dog than choking him with pudding.” Although why a dog would choke on pudding, I can’t imagine.
In 1678, in the second edition of John Ray’s collection of English proverbs, he gives the phrase as, “there are more ways to kill a dog than hanging.” That is certainly more lethal than choking on pudding.
Another printed citation of this proverb is in an 1840 short story by the American humorist Seba Smith, The Money Diggers:
“There are more ways than one to skin a cat, so are there more ways than one of digging for money.”
In 1889, Mark Twain published A Connecticut Yankee in King Arthur’s Court, in which he wrote: “she was wise, subtle, and knew more than one way to skin a cat.” In other words, she knew there was more than one way to get what she wanted.
The American English term ‘to skin a cat,’ means to perform a gymnastic exercise that involves passing the feet and legs between the arms while hanging by the hands from a horizontal bar and pull oneself up into a sitting position.
Why would you skin a cat? To make money. In the 18th and 19th centuries, cat skins were valuable, and used as a cheap fur trimming and also to make felt for hats.
In the southern US states, the phrase is often used to refer to catfish, a fish that is usually skinned before cooking but, since catfish do not live everywhere, this is just a local application of the proverb.
Being a cat-lover, the talk of skinning one would make me wince if I didn’t know there was no possibility of accomplishing that on a live cat. Those claws can be deadly.