Forgot to measure the diameter of the couple I took out, very small, but the ones I have are not screw threads so to speak but are a somewhat coarse thread self taping type screw. What I would call a "sheet metal" screw. Length under head is about 7 to 8 mm.
If it was me I would take cap to hardware store and try a few screws till I found one that fit. Or it you have a motorcycle junk yard near you start looking there.