Hi mphansaria,
a warm welcome to Flyertalk FT.
Just to clarify: Switzerland in not yet a schengen country!
There are luggage locker facility at the Zürich Airport RailwayStation and they cost 7 CHF a day for the big and 5 CHF for the small locker.
However, they can only be used, as I recall it, for 72 hours.
At Zürich Mainstation, I think, there is a "Gepäckaufbewahrung" (0512 22 29 04), where you might be able to leave it for longer.
Enjoy Europe in 11 days