If the cats get up on the sink (oh, you think they don't, eh?
), you might try what I do.
Sincel 9/11, I am more careful what I leave for the animals, just in case I am very late (days) getting home, as I live in earthquake/volcano country. Besides the two big bowls of water for the dog, I leave a plastic grate in the bottom of the sink and set a stainless steel bowl under it, and let the faucet drip slowly into it. With the grate, I don't have to worry about the bowl shifting and plugging the drain, coming home to a new kitchen swimming pool. The cats like the drip. Even if the power goes off, the water still runs (ours, anyway -- not if you have a well, I guess).
BTW, for a sick-cat treat, I discovered that since my cat likes cheese, I keep a can of cheddar-cheese condensed soup in the pantry. Considerably diluted, they will often take it if nothing else is appealing.
Re: the tuna juice. I was just thinking of it for temporary situations. Cats are incredible creatures of habit. If you give them something yummy occasionally, they're fine with it when they're sick. But if it's entirely new to them, even tuna water, they may turn their noses up at it. So I give it to them just occasionally as a treat. A bit in hot weather can help keep them hydrated, as a dehydrated cat IS an emergency.