I also have this.. I have had it for a while, so I don't think it's just menopause, although I'm sure that's part of it. It's very much on my face, and the smallest exertion, literally getting up to sort the air conditioner out and fighting a bit with the hose and the window, will have me dripping for ages from my face. It stings my eyes and drips onto papers etc. I use fans and air con when I can but I try not to.
What can help a bit is a prescription wipe called 'Secure' wipes, glycopyrralate, which you can order online from pharmacy.ca - you fill in a form and they discuss it with you and then post if suitable. It doesn't get rid of it but I think it helps, but it takes a day or two of use first. These were recommended by the hyperhidrosis site.
There are some prescription medicines, but I worry about the dryness elsewhere as they are anti-cholinergic; I also worry about increased demetia risk from them, so don't want to try them.
I've ordered perspi-guard wipes from amazon, but not tried them yet as I still have the Secure wipes.
None of the other types sold in boots etc made any difference.
The Carpe stuff has been advertised a lot on my FB but I haven't tried it yet - glad to hear a good review here, as I read mixed reviews about it for the face, a little worried that it just turns into a paste if you sweat a lot.
Haven't tried HRT, yet, though I'm considering it. I have hypertension well controlled by tablets, but I also get occasional migraines, which are coming back a bit when I have a very occasional period now, and I am not sure I want to return to having an actual monthly bleed like you would with HRT, alongside the more sudden drops in progesterone that you'd get from the cyclical HRT routine; I've heard that a lot of people find that quite difficult to get used to, and if I'm already sensitive to progesterone levels and potential migraines, I don't know if I want to add to that and possibly start having a lot more of them - it's been a bit of a nice relief to have had hardly any migraines for a decade or more now, and only occasional periods for the last year or two, so I'm not sure I want to mess with that just yet. But the facial sweating is pretty unpleasant when it happens, but that is likely to happen to a fairly great extent with or without HRT. So I'm still a bit undecided, like you.