I once ordered a set of all three, 4-40, 3-48 and 2-56 in brass, slotted round head.
Don't remember where they all got to now.
So I just checked, a frame had broken off screws (ugh), so I drove them half-way out with a roofing nail, and then sacrificed a brass #3 screw to hammer them through. The #3 is about the right size, but the steel threads were more like coarse sheet-metal screws. So my brass 3-48 screws (with bronze washers) into painted holes might be faking it, and could fall out any day.
I have also been thinking about getting a set of extra-small screw taps, for such purposes.