I'm not looking this up, of troy--just taking a blind stab.

Cats can walk easily at great heights and still maintain their sense of balance--high walls, ledges, limbs of trees. They maintain their balance and poise nearly always.

I would guess that walkways perched high came to be known as 'catwalks' because the cat does walk so gracefully at heights.

I've been involved in theatre nearly my whole life and have always heard about the catwalks above (and sometimes around and above) the stage. There's another term I've heard for an area accessible to the light techs, but I can't think of it right now. Maybe Juan can provide it. But you do hear 'catwalks' regularly around theatres.

And your other comment about the hallways that are outside apartments. Could they be referred to as 'breezeways'?