If you want to travel to a destination outside the ZVV coverage area by starting your journey on a ZVV ticket, you must purchase a normal SBB ticket starting from the last stop on your concrete route that is still part of the ZVV area. In other words, the train you're on must stop at the station where the SBB ticket originates, zooming through on a faster train using the same route doesn't count.

Buying such a SBB ticket is very simple, and can be done at any SBB vending machine in Switzerland. There is no issue getting a SBB ticket all the way through to Singen including the DB portion (or the bus from Stein am Rhein to Singen). Just choose the "ticket from another station" option and enter the desired departure station.

However you first need to know where the switch from the ZVV day pass to the SBB ticket will occur on your concrete itinerary. When you run a query for Zurich HB to Singen on sbb.ch, you will get a bunch of different routing options. Some of them indeed use the S9 route via Rafz that you mentioned, but others use nonstop trains from Zurich HB to Schaffhausen. For the former, you would purchase a SBB ticket from Rafz to Singen, while for the other you would need to purchase a SBB ticket all the way from Zurich HB to Singen.

If you want to maximize your ZVV day pass usage, you should choose a routing that utilizes the S29, which remains within the ZVV coverage area all the way until Stammheim, just outside Stein am Rhein. So you would purchase a SBB ticket from Stammheim to Singen (CHF 9.80 one-way full fare).

Hope this clarifies.