If I were you, I wouldn’t bother about buying the Half Fare Card in advance. You could just buying it at any SBB Travel Center upon arrival in Switzerland. Just bring a passport photo or an equivalent online face picture for the card. Buying it on-site would also ease the distribution of the SwissPass card which is preferably sent to a Swiss address, e.g. your students’ home stay.
For the first days, until the card has been dispatched to your address, you will get a temporary card in form of a paper document with QR code, to be used with an official physical ID document that can be your passport, state ID, or driver license.
You may wish to write a pm to user @Ex-Bähnler, perhaps he still has some vouchers left that give you an additional CHF 33 reduction on the first purchase of the Half Fare Card.