Your dog will be fine. I know people who put small amounts of chlorine in animal's water in order to keep bacteria, etc., to a minimum. Once a dog drinks out of it's water bowl/dish/bucket,...
The only info I could find on copper water bowls, was from sites selling copper water bowls. They claim that Copper is scientifically-proven to inhibit bacteria growth, but I couldn't find anything...
Only as much as it would hurt a human. But you have to remember we know why we are getting the injections while some dogs might get confused and therefore scared as they are oblivious to whet the vet...