I built a connector that replaces the screw on tip that goes on the kitchen fawcet. You will probably find that the thread is not a standard plumbig thread and that the threads are different for each make of shower fitting. The fittings for the fawcets are available from the places that sell those stupid filters that screw on to the kitchen tap to give you "pure" water. You may be able to make something up with a combination of fittings from the filter place, plumbing fittings including the flexable plumbing hose that goes under your wash hand basin and the snap on garden hose connectors to your hose. Your idea is good and mine works well, but off the kitchen. It allows you to blend water to get the right temperature without hassle