I do not use a shoulder screw. I use a #10-32 screw and sandwich a nut between the mounting plate (see the LASER_CAR_ASSEMBLY). #10-32 is almost exactly the right size. I have to sand down a half/thou on some of the screws. Typically a shoulder screw is not used because you never want the inner race to be able to spin. The more common method is the eccentric shaft (see image) that allows you to tension the bearing against the rail.
Bishop Wisecarver is the inventor of these things. You can get some info there.
These guys sell them cheap, but not the 3/16" size.
f you really want a shoulder screw, I usually get them at Stock Drive.
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