I also doubt very much that a cat would swallow a battery.

I do just want to ask one thing, as this is the type of thing I would do; are you sure a battery was in there? Is this an electric clock with battery back up? I have been known to remove the battery to buy a new one and . . . . well, you get the idea. If this is a battery operated clock, well then I guess there was a battery and now it is hiding somewhere.

Hoping you find it soon!