You can take it on board a train provided there is enough space. It will require a bicycle ticket, which is either a half fare point-to-point ticket, Kreuzlingen-Zürich Flughafen, or a bicycle day pass, in either case, they cost you CHF 14.00. Bicycles are transported free of charge if done so in a TranZbag, only.
Google knows two bicycle shops in Kreuzlingen, Velo Rüegger AG and Bike Laden GmbH. You may wish to ask them upfront concerning available boxes. If they don’t, you will for sure get it at the Swissport Ticket Desk in Check-in 2 at ZRH Airport.
More on the topic: https://www.sbb.ch/en/timetable/travel-advice/bicycles.html