Have you tried a facial epilator? The Braun 830 is specially made for facial hair and has been pretty effective in my experience.
There’s also facial hair trimmers if its more peach fuzz that you’re dealing with. There was a product called the Panasonic Facial Hair Trimmer that might work for you. It’s super discreet and should keep the peach fuzz at bay, plus way less painful than epilating or waxing 