They don't specify small screws anywhere else in the design? On the Sonex, they use #4 x 3/8" long screws directly into the external skins to secure cover plates. These are on the outside of the airframe, and they don't loosen up in flight. In the plate, drill #30, then a very small hole in the base part. I forget what the small hole size was - maybe 1/16". Use your favorite vendor, but here's a Spruce part number to look at:
T4X6 4X3/8-A-TR-PH-SS SHT MET SCREW