You could indeed get the Half Fare Card. You may consider getting it for both adults, as the HFC does also give you 50% off on mountain railways. I assume you are not going to Zermatt just to sit in the hotel pool.
Normal tickets are for a route, not a train, so you can buy a normal ticket in advance and then just proceed to take the next train to your destination once you are out of arrivals. Such tickets are the same price bought in advance or at the moment of travel itself, so the main reason to buy them in advance is just for convenience. I used to often buy the ticket while waiting for my luggage. There is a ticket vending machine in the luggage ares. Nowadays I use my mobile.
Another good option for when one arrives by plane is a saver day pass.
Just go to www.sbb.ch and look up times and prices for your date. You will notice multiple offers.
- Point to Point ticket: Fully flexible and refundable. Ticket is for a route, and you can travel on any train on the route you want to get to your destination.
- Saver tickets: Limited to a particular train.,
- Day passes. If a day pass is available for less than the price of point-to-point that is also a good option, as that is fully flexible as well. But the saver day pass is not refundable.