“There’s more than one way to skin a cat” means that there are more ways than one of doing things. John Ray’s A Collection of English Proverbs (1678) included “There are more ways to kill a dog then hanging.” An 1835 newspaper included, “There is an old maxim, that ‘there are many ways to kill a dog;’ and “there are two ways to drown a man.’”
 
“At any rate, thought I, there’s more than one way to skin a cat, as a butcher would say” was cited in print in January 1836. A similar expression (cited in print since the 1950s) is “There’s more than one way to peel an orange.”
 
 
Wiktionary: there’s more than one way to skin a cat
Proverb
there’s more than one way to skin a cat
1. A problem generally has more than one solution.
 
World Wide Words
Q From Mike Reilly: Anything interesting in the origin of There’s more
than one way to skin a cat?
A To a lexicographer, all phrases are interesting, it’s just that some of them are more interesting than others ...
 
There are many versions of this proverb, which suggests there are always several ways to do something. Charles Kingsley used one old British form in Westward Ho! in 1855: “there are more ways of killing a cat than choking it with cream”. Other versions include “there are more ways of killing a cat than by choking it with butter”, and “there are more ways of killing a dog than choking him with pudding”. The earliest version appears as far back as 1678, in the second edition of John Ray’s collection of English proverbs, in which he gives it as “there are more ways to kill a dog than hanging.” AN 1835 weekly newspaper printed, “There is an old maxim, that “‘there are many ways to kill a dog;’ and ‘there are two ways to drown a man.’”
 
(Oxford English Dictionary)
skin, v.
orig. U.S. there is more than one way to skin a cat and variants:
there is more than one means of achieving a given aim.
1847 Independent & Amer. Gen. Advertiser (Platteville, Wisconsin) 11 June 1/5   There are two ways to skin a cat, and two ways to win a heart.
1880 18th Ann. Rep. State Board Agric. Michigan 215   Usually, as the old saying is, ‘There is more than one way to skin a cat’—more than one method of producing the same result.
 
Google Books
A Collection of English Proverbs
By John Ray
Cambridge: Printed by John Hayes
1678
Pg. 127:
There are more ways to kill a dog then hanging.
 
Google Books
18 April 1835, Niles Weekly Register, pg. 125, col. 2:
There is an old maxim, that “there are many ways to kill a dog;” and “there are two ways to drown a man.”
   
30 January 1836, Logansport (IN) Canal Telegraph, pg. 3, col. 1:
At any rate, thought I, there’s more than one way to skin a cat, as a butcher would say.
(From the New-York Transcript—ed.)
 
19 March 1836, Phoenix Civilian (Cumberland, MD), pg. 1, col. 3:
At any rate, thought I, there’s more than one way to skin a cat, as a butcher would say.
 
Google Books
August 1840, Burton’s Gentleman’s Magazine and American Monthly Review, “The Money Diggers” by Seba Smith, pg. 81:
THIS is a money digging world of ours ; and, as it is said, “there are more ways than one to skin a cat,” so are there more ways than one of digging for money.
   
Google Books
Yankee Humour, and Uncle Sam’s Fun.
With an introduction by William Jerdan
London: Ingram, Cooke, and Co.
1853
Pg. 72:
There are two ways to skin a cat, and two ways to win a heart; two ways to put on a shirt, and two ways to make a shift; two ways to tell a story, and two ways to bestow charity; half a dozen ways to destruction, but only one way to heaven—and that way is as much narrower than Theatre Alley as a sheep-path is narrower than the Third Avenue.
   
Google Books
A Connecticut Yankee in King Arthur’s Court
By Mark Twain
New York, NY: Harper & Brothers Publishers
1889
Pg. 65:
But then the Church came to the front, with an ax to grind; and she was wise, subtle, and knew more than one way to skin a cat — or a nation; she invented “divine right of things,” and propped it all around, brick by brick, with the Beatitudes ...