... voltage drop across them would be 1uV ...
And you're ok with that?
Well, I'm disappointed in all of you splitting hares
over the whole thing if you're not going to take the R
Thévenin of the source into account which, calculating from the datasheet's output regulation figures, might be as high as \$100m\Omega\$, on the same order as the resistance posited for the test leads (Which by the way, from previously having measured my collection of test leads, is likely to be close to \$20m\Omega\$).