This is a transit outside of Schengen. Not entirely sure if you will need to go through security again to enter the departures area, but I think not as Romania is EU.
If you don't want to enter the Schengen area, while no lounge is open overnight, you can just lie down on a bench, or pay for a room at the transit hotel. I seem to remember there is an option to pay (less than the price of a room) for a more comfortable couch.
Otherwise you can enter Schengen and get a proper hotel (or go to a nightclub or sleep on the street or whatever); there is a Radisson which is connected to the airport and many other airport hotels accessible by shuttle.
Train to the city centre takes only about 10 minutes so it could be faster than waiting for a hotel shuttle. You can get a 24 hour ticket which is basically the price of two one-ways and that will also let you use all other public transport, it's a bit costly but perhaps the cost will be offset by a cheaper hotel than the airport offerings. Of course it's Zurich so a nice hotel will be expensive.
Very good info thank you.
If you don't mind asking, what/where is this transit hotel that you mention?