For fee, sure
I dont have an answer to the lounge access question, but...
There is at least one location at ZRH where one can take a shower for about 9 CHF. They provide you with towels and the showers are quite nice. It has been over a year since I was in ZRH and I dont remember where the showers (exactly) are.
Alternatively, it is always possible to buy a daypass to most airline lounges. Some if not all of these will have showers.