HAIR LINE MICS AND SWEAT
We like to use a bent paperclip or a wire with about the same gauge (found in craft stores) taped to the mic cable that is bent around to fit the ear. (It's way cheaper than buying the expensive manufactured version) It can come down closer to the mouth and shouldn't be affected by the sweat. If you use flesh colored tape or makeup it should blend in pretty well, and shouldn't be a visual distraction.
If it's in the hairline you should be able to get it with some combination of toupee clips and elastic. Further down the forehead consider toupee tape (which may sweat off) or spirit gum (which will not sweat off, but isn't the best for the mic either). You could also try applying a large piece of surgical tape directly to clean dry skin, and then taping the mic to that tape. The idea behind surgical tapes like Transpore is that the patient (performer) will sweat through the tape... instead of sweating off the tape. This only works when the tape is applied to clean dry skin. Use an alcohol swap on the area to be taped.
Attach a loop of elastic string to the mic. Size the loop to fit the actor's head. The actor puts the loop around their head like a hat band, combs hair over it (or uses bobby pins/wig clips if preferred) and the mic is positioned mid fore-head. Your wardrobe people might have elastic string in stock already (it looks like a big rubber band that is fabric covered). If needed, the actor can easily pull it off between changes, but a better bet is to simply let the mic wire dangle down the actor's back under the clothing and have the belt pack worn in the small of the back. You can run the mic wire over the top of the head or have it follow the path of the elastic string over one ear. Can be worn under fast wig changes too if you run the loop and mic wire under a wig cap.
For a show with stickers placed on actors' faces, I had the sweatiest ones dab antiperspirant on the spots beforehand. It worked great.
Be sure to have a can of spray air backstage for blowing the sweat out of the mic element. Also be sure that the mic is muted before doing this... At my last venue we had the sweatiest actor ever. He could drench a mic pack INSIDE a latex wrapper, and the tips of the mic element would be filled with sweat before the 2nd number. So we wrapped the pack in cotton AND latex, and had air to blow out the sweat backstage. Sorry, no advice on how to keep it ON him...Be very cautious about blowing out mike elements, especially with compressed gases of any sort. The diaphragms are not designed for such punishment and it will void any warranty if you damage them. Specifically, be sure to spray across, not in to the element.
The only way that I'll blow out a mic screen is from the back. Other than that, I'll soak up the sweat with a q-tip, rinse with distilled, and soak it up again. A good screen will hold the sweat and the water and keep it away from the diaphragm, and blowing across it can blow sweat into the diaphragm.
Also try using Tegaderm-brand surgical tape/warps. We would get the big IV squares, then cut them down into little strips. It is much stickier than first-aid tape, completely clear (so you can stick it anywhere & it's not seen), plus stretches a little for better application. Check your local hospital supplier.