I think the saying is actually: "There are more ways of killing a cat..."
It's an phrase that's usually left unfinished, but my mother always added: "...than choking it with butter."
Sadly, cats are being skinned as you read this. They are skinned and dropped in boiling water and eaten. They are not put to sleep before this happens. There are country's that consider this Ok.
Old saying - current truth.
According to informed sources....
The first time the phrase appears to have been used was in the the Charles Kingsley book Westward Ho! in 1855, and then it was recorded again in Mark Twain's book A Connecticut Yankee in King Arthur's Court.
Of course it may not refer to feline cat's anyway. There are plenty of websites in the US that are devoted to skinning cats ' but they refer to the giant catfish that abound in them thare parts.
The phrase originates from the British Royal Navy. The "cat" referred to is a Cat-o-nine-tails whip used to punish sailers. Some whips had bits of metal embedded in them. A VERY unpleasant job was to remove the human flesh from the whip after the pusinhment was meted (to keep from ruining the whip). Therefore, people would get very creative about cleaning the flesh from the whip (this was called "skinning the cat"). The phrase refers to peoples ability to find different ways to get a job done.