OP, I am perimenopausal with thyroid issues. Light skin, dark hair on head, tache and chin, blond peach fuzz on cheeks. Dark moustache, dark spiky rapidly growing hairs on chin and neck, too many to effectively pluck. Hair removal creams blistered my skin so that was a no go; waxing was hell and caused breakouts. For the longest time I just shaved tache and chin, every morning with a proper Harry's razor and creamy facial cleanser and that worked semi well. It really doesn't make anything grow back fuller or faster.
Early in the summer I got the absolute basic model Lumea (not the gun style, the one that looks like an electric razor) on a half-price sale. After 2.5 months of using every other week I've gotten pretty much rid of moustache, and reduced the chin hairs a lot. (As they are hormonal I know IPL won't do much for them.) I still swipe my chin with razor each morning to make sure no chin hairs are showing, but really it's much much better, so much so that I could probably get away with minor plucking once a week. Every so often I do my peach fuzz on cheeks as well; tache is pretty much gone. I'm more impressed by the Lumea than I expected to be, and I'm sure a newer model with a facial port would be even better.
The key with shaving is, I think, use a good razor, rinse and dry thoroughly between uses, change blades or razors frequently, and don't be self-conscious about it. Better to shave in private at home for 15 seconds each morning, when you wash your face, than to find those horrible bristly chin and neck hairs in the middle of the day in public.