As far as I know, this is a piece of sailor's talk. The cat being swung is a cat o' nine tails -- presumably the expression originally referred to cabins which didn't have enough room to 'swing a cat' in.
It refers to a old (and not defunct) tradition of quite literally swinging a cat around by its tail in a new house (bearing in mind that many "houses" in 16th century England were little more than rooms.
This was supposed to bring good fortune upo. the inhabitants.
(Source: London: The Biography - Perter Ackroyd)