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Jamie the ones I linked will be right between the two smallest you posted

at about 3.1mm

This is another source but you have to call them about the tiny ones :( which for you is a bummer.....

Jamie the ones I linked are only 1/8 diameter so the peen pretty much covers the washer after you are done, not sure if they get much smaller they will even hold onto the washer

Might be better to...

There is one other supplier of the small SS washers but they are basically the same size as the ones from Microfasteners I think they might be thinner and weaker but not a smaller Diameter :(
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