While I shave the whole mustache area, I do have some issues with those same area (again really fine hairs). What I found that works for me is for the corner areas (and rest of mustache area) is to actaully pull my nose over in the opposite direction while while keeping mouth open. I don't me hold the tip of your nose but have 3 fingers holding near the base and using you hand to bend it over. It seems to help pull those corners up and to the side and makes those hairs stand up so the razor can get them.

For the lower lip I just fold my lip over my lower teeth and have my mouth in a grimace; again it gets those hairs to stand up. I do have to go ATG to get a good shave but if you take it slow and practice it it is actually quite easy and have never had an issue with blade slipping into my lips.