I think the screws are phillips- I have never seen anything else in all the ones I've done.
I'm switching mine (1982) to an electric on the passenger side. I broke my manual one and had an electric one available, so I'll run some wires and voila, no more reaching over to adjust, I can pretend I'm just like all you guys with 83 and up mercedes
(Also switching over the newer style dome light as well!)