Except for the shops of Swisscom, Sunrise and Orange in the public area ("Airport Shopping Plaza") there's no place to buy SIM cards at Kloten airport. But distances are not too far - I think 20-30 minutes should be enough to get a SIM card and pass security check again.
When buying a SIM card in Switzerland you are required to show your ID for registration, however you don't need to be a Swiss resident.
If you want to get online in Switzerland I would recommend a Swisscom SIM with the "Natel Easy Be Free" prepaid plan, which gives you unlimited internet access for CHF 5 per day (for details check
Switzerland - Swisscom - Prepaid Wireless Internet Access), which is significantly cheaper and more secure than the unencrypted WiFi network at the airport.