My wife has a Brit water container in the frig for her drinking water. I don't see why you don't eliminate the water softener completely if you're on city water.
If your complaint is about dry skin in the winter that comes with the territory of where you live. I even suffer from it here in NC. legs get itchy from my socks etc. Of course my wife is always yelling at me about it. Thus the lubriderm by the gallon.