You are correct in saying the system doesn't overflow. However, one who removes the cap and finds the level lower, one will most by natural instinct add water. Crank up engine, and if a 16 lb cap is not installed, it punks out.
The washer fluid container is ideal as boodlefoof suggests. The washer bottle top has a hose going from the nipple on the bottom of the cap to the bottom of the tank. I use mine for the same purpose. Only I have a 22 lb cap, so, I don't have to worry too much about overflowing, just bursting a hose. If you're gonna do it, do it right!!
All I can say is "Real race cars don't have wipers." Hence, no need for washers.
However, all is not lost. There are aftermarket overflow tanks out there for the use. Kindda cheesy, but, doable.