In the spirit of trying to help, they do make in-cage water bottles big enough for cats - you know, like the bottles you give rabbits. And you can buy ones that hook inside the cage so the risk of it falling would be minimized. Fasten it to the cage door with zip ties and I promise it won't fall.

I'm always appalled that the little tiny bowls that clip onto the door are considered adequate - really, I don't see how that's possible. I had the most spoiled military working dogs ever because they always had one of those bottles clipped to the door instead!

That said, I hope you're able to get your kitty inside with you as much as possible!