Your hotel is in Vevey, not Montreux, so you need transport from Vevey. Hotel Moevenpick Zürich Airport is in Glattbrug, and neither in the city or in the airport. If you are flying the next day I would suggest you stay at the Radisson Blue, or the Hyatt Regency at the airport itself.
And travelling by train from Vevey to Zurich Airport is trivially easy: Go to station. Buy ticket. Travel. There is nothing to “secure”, and you just take your luggage with you.