Here's my single tub setup



The lid locks down tight and even if a cat did manage to knock it off the dresser, I doubt it would open. (It's a 30 gallon Rubbermaid I bought at WalMart for... $8, I think?)

Besides, by design, the tub you would want to keep a BP in would be wider and longer than tall and those are pretty hard to knock over, especially if you end up getting something like a ZooMed heat pad they come with feet that have the handy side-effect of making the tub harder to move around.

You are being paranoid, but if you really want to do it, I'm not going to be able to stop you.