gradual escalation
I tend to use a gradually escalating approach. Given that (I think) you have a screw that goes into a plate nut on the inboard skin lip of the wing, you don't have a lot of support to bang away with impact methods like the Screw Knocker or impact drivers.
The tip that Mike recommended, or the Anti Cam-out Ribs may work.
If not, my next move would be to saw a straight-blade screwdriver slot with a dremel. Use a really good screwdriver.
If that strips out, or twists the head off the screw, then you have to drill it. First stage is to drill small and try an Easy-out. If that doesn't work, then step up in drill sizes until you have drilled almost all of the screw out. How close you can get depends on how well centered your hole is. I've gotten to where there is just a thin sleeve with the threads, then I try to grab a corner of the thread and pull with a needle-nose pliers. Sometimes you get lucky and the thread piece of the screw just unwinds out of the hole like a spring. If not, get some clean thread showing and use a tap to chase the thread.
You can try to not run the tap all the way, so as to preserve the locking feature, but you may have to face the idea that in order to restore the threads, you might have to lose some or most of the locking feature. Lesser of evils. If you don't mind the risk of the screw backing out (it is just one screw in a fairing) then just tighten it well and check it on pre-flight. If it is more important that it not back out, use a star washer under the head, or Locktite.
Ultimately, if you have to drill so much that the threads in the plate nut are really shot, then when you get the fairing off, replace the plate nut.
Then, from now on, use Mike's trick and put some wax on the threads of fresh screws.