try a different slicer.
prusaslicer is a good place to start.

Also check extrusion settings. Most printers work accurately best at somewhere between 85-95 % extrusion ratio.
Then there's print speed and printing temp.

There is no reason you cant print 0.6mm with a 0.4mm nozzle.

Though you might find setting edge width to 0.5mm works better.

Also have you measured the actual extrusion diameter ?
Get some digital calipers, extrude a length of pla, let it cool and measure the actual extruded diameter - there should be somwhere in the slicer to enter that information (I don't use cura - can't stand it) but the setting should be in there somewhere.

You will most likely find that the actual diameter is larger than 0.4 but smaller than cura has it already set to. This will effect the extruded width of a single wall.

Between getting that right and playing with the extrusion ratio, you should be able to get a accurate edge width.

It also depends where the edge is on the model - got an stl ?
I can try it on my machine with simplify 3d.