The story
Origin unknown. Other proverbs with the same meaning referencing the killing of animals are also attested, some as early as the 17th century; see, for example, “there are more ways to kill a dog than hanging” (1678), “there is more than one way to kill a cat” (1833), and “more ways of killing a cat than choking her with cream” (1855).
Etymology from Wiktionary, CC BY-SA 4.0.