tickets – Train from Geneva Airport to Fiesch

I see no reason why you could not do it. There are ATMs and workstations in the Geneva airport station. As long as you have money or an acceptable card, this should be pretty simple.

There are two trains per hour, so even if you have to queue a little, that should not be a problem.

However, I do not see any reason for not being able to buy tickets online. Have you tried sbb.ch?