Ok, but that doesn't mean it couldn't have a 4mm hex nut. The 4mm refers to the hex wrench needed to turn it, not the threading/width of of the rod.
Very unlikely that anyone would ever produce a nut with standard threads and a metricwrench fit.
The wrench for a 10-32 would be INSANELY close to a 4mm, so yes a 4mm would/should fit.
But if the nut is "Standard" and not Metric, then it takes a Standard wrench.
Thats industry standard for fasteners.
BUT, a 10-32 uses a 5/32 allen wrench. Which is .1563". Which is 3.96mm.......
So, yeah, a 4mm should work in most, if not all cases.
.04mm is NOTHING considering how massive the tolerances are.
It may fit one bass. And yet on another it may not.
And not sure where they source their rods from for the EURO models, so it could be a metric rod.
Sorry, just the M.E. in me coming out! And being a little OCD about nuts as I've garffed up way too many over the years!