I can't swing a dead cat without hitting some kind of war memorial or something.
More in the nit-picking spirit of the original post, here is the "cat" being swung:
The "cat o' nine tails" is by definition not a living thing to begin with, so saying "swing a dead cat" is redundant (or something).
Some nitpicking of my own. I've always understood "swing a dead cat" to mean lots of something in a small area (i.e. if I were to take a dead cat by the tail and swing it around I would hit whatever it is I'm talking about - e.g. "At the court house you couldn't swing a dead cat without hitting a lawyer"), as intended in the original post.
While I suppose the saying may have originated meaning the whip, non-navy people may have realized that. The reason the cat is dead, I have always supposed, is that swinging a live cat would just get you a bunch of claw marks

Now why would people assume a cat meaning an animal? I can think of no other reason than the same reason there is more than one way to skin a cat, but that might be letting the cat out of the bag .