Toilets, Sinks, Showers, Tubs and Disposals - Outdoor Shower

I installed an outdoor shower on my deck. It is from Orvis but it has a single handle and a hose connect designed for only cold water. I plumbed it with hot & cold from my basement piping using a "Y" designed for converting one hose to two hoses with a shut off on each arm. I installed it in reverse with hot coming into one arm and cold to the other - mixing at the hose connect on the shower. I now find that the hot water is migrating into the cold water line back to the house plumbing unless I turn off the shut off to the cold line. Will a one way valve on the cold line solve this problem?