If your water heater is in good condition you should be able to use a mix of hot and cold water for water changes. Tap water is treated so its pH is always high enough not to corrode copper pipes, which means it doesn't dissolve any copper into the water. Heating the water in a water heater doesn't change that. Further, water heaters use a sacrificial anode to prevent corrosion of the liner or copper parts, which is another defense against copper getting into the water. Any copper that gets into the water can be eliminated by running the water for a few minutes to flush out the standing water, before starting to use it for the aquarium.
When I had Cherry Shrimp I continued to do water changes, using a hot/cold water mix and the shrimp continued to reproduce rapidly.