I need to move around Zurich but it's not really urgent, so I wonder if there is some popular billboard where I can post my "requirements" and receive offers.

To be specific, I will be fine with short-term, maybe also workweek only, don't mind if out of the center or in a close village if good public transport, good for remote working, 2 people.

In other countries, there are billboards where seekers can post too. I wonder if there is something similar in Switzerland.

Coop and Migros usually have them (as your range is rather big, that will be a week's job to put them up ).
Many people also place flat-search up on tutti.ch.