But exposing yourself to the arts in New York is pretty easy — you can’t swing a dead cat in Midtown without hitting an oboist or ballerina — and who knows, you might even enjoy it.
From Gridskipper (read here)
Must be a lot of oboists in Midtown these days, eh? But why would anyone enjoying hitting an oboist with a dead cat? Ouch!
“dead cat” is a corruption of the original — an old naval expression –“Not enough room to swing a cat”, where the “cat” was the cat-o-nine-tails that would be used for discipline. (I doubt the disciplinee enjoyed it.)
So, the “dead” part was inserted by somebody using the expression in a formulaic way, without visualizing its meaning.