My apologies if I am in over my head here...
Try this link:
McMaster-Carr
Or here for button head screws:
McMaster-Carr
Scroll down a bit to see brass M3 x 0.5mm screws in different lengths [5-20mm] on either link.
I hope that helps!
Thanks. I really like McMaster Carr, particularly their ordering system. Although a few years ago they refused to ship abroad to me. Something about US export controls.
They don't have brass screws with a head 4mm or less. I would have to get 18-8 stainless, which is not salt water corrosion resistant. I may have to resort to @axxel57 's solution of reducing the head size.
Also their metric screws are considerably more expensive than the imperial equivalent, and hex screws in both are understandably much more expensive than slotted screws.