I laughed when I heard cat-honey. I've got 2 cats, and the one thing I have not seen is cat-honey in the sand boxes......
I control the itches, acquired way late in my life, w/ a cortisone ointment, knocks it down almost right away. Neutral clothes detergent also...
For the shower question, you are forcing in a foreign substance at greater pressure than the water, unless using a passive feed..venturi I believe. The answer, like at a car wash is you need to introduce a Reduced Pressure Differential Device, which is the only mechanical device rating as high as a proper Air Gap. Passive feed may only require a lower rated device, say a double check with vacuum breaker, or even less. IDK. You install a backflow device in your connection to the potable main.