If this were in Germany, you would not be able to. SparPreis tickets are only valid for the specific train listed. I doubt that Switzerland would make any exception. You should have thought of this before you bought a specific train ticket. You could probably have built in a stopover of, say, 1 or 2 hours at Zürich HB.
Also, in Germany, you could have specified a route that uses a regional train, example of the many S-Bahn that runs from Zürich HB to the airport every few minutes. Regional trains in Germany are not train specific; you can use any other one on the same route anytime that day (actually until 10 am the following day).
However, I don't know how Switzerland honors German Rail tickets. They might be more flexible; they might be less flexible. They might let you take any S-Bahn to finish the route. You'll have to ask the conductor on the train arriving at Zürich. But, then, that train is a German ICE, so that conductor might not know. If you are going to make a stop in Zürich (town) anyway, make a quick stop at the ticket counter in the HB to find out, before getting on the train and risking a possible fine.