I think either one could work for you without harming the fish.
You could use bottled water and treat it like tap water. Since that's basically all it is. The only problem I'd see, is if the company puts in certain minerals to enhance the taste. They could mess with the chemistry of your tank, though probably not noticeably.
On the other hand, distilled water would be low on oxygen content, which you can shake the bottle before using it to help get some of the oxygen back. Either way, I'd probably still put in a bit of tap water conditioner just to be safe. Maybe half of the normal dosage.
I would try to hold out on doing any serious water changes for the time being. Your fish aren't going to be put in mortal danger by doing a water change a week late. Do about a 5-10% water change to pull through this week, and then go back to a 10-20% water change several days after the water has been declared safe.
Other than that, I'm not sure there's anything else you can do for them, just don't expose them to the chemicals.