Mum of near 93, hates face hair.

Walmart has one for $10, battery powered and works well for elderly with arthritis.

From the way you have worded this I am guessing mom is in a care facility.
Use the lady shaver they have. You can ask how to clean it after you use it. Most are pretty easy to take the head off, sweep out any hairs and pop the head back on. (I would clean it before you use it, if it looks like it has never been cleaned before I would bring my own, if you do not have one do not spend a lot of money on one and there is no real difference between "women's and men's" razors.)
You can bring your own (this would be my preference) there are very small ones that look like a lipstick and there are large ones that are full size razors.

If there are just a few hairs she is concerned about you can "simply" pluck them .. slightly more painful though.

I hate facial hair as well and I'm only 65, soon to be 66 in a few weeks. I use the Pop Sonic Smoothie to remove my unwanted peach fuzz on my face and it works great. You just rotate it all around the areas that have hair that you want to remove. There are of course other companies that make similar items, so you may just want to "Google" to view your many choices.

I found the simplest option was to shave my mom about once a week, but it's really going to depend on how fast your mom's facial hair grows. (Ain't aging grand?🙄)