I like the replies suggesting pure malts. In my experience, as a physician, the most logical cause of traveller’s sore throat is the proximity to fellow travellers carrying throat viruses. How often do you sit down and the next seat passenger gets out a handkerchief and starts blowing his/her nose?
I can’t quite see why a dry atmosphere should cause a sore throat for days after the flight.
Other than the astringent effects of pure malt, I suppose you could try an Asian-style surgical facemask, but these are incapable of filtering out viruses.
I’m afraid that minor viruses are an unavoidable element of air travel!