I need to widen the rear sight notch on a fixed-sight revolver by about 2mm. Any ideas on how to do it without it looking like some crackhead did it?

Grind the teeth off one edge of a good quality small file so you can slide that edge across the bottom of the sight notch without deepening the notch. You of course want a file with the finest teeth offered. I think mine are around 4" long including the tang. They aren't where I'm at to measure but they are a standard size. Nicholson is a good brand. I might have dulled an edge on mine with a knife sharpening stone. It's been so long that I forget. Running it past an electric grinder you might not wind up with a straight edge.

Go slow and eye ball your progress frequently.

Edit to add. Very precise file work can be done. I once installed a factory adjustable sight on a Model 36 with only files, a drill and a tap. You could not tell it was not installed by S&W.

k22fan has the right idea but there is no need to grind off the teeth of a file IF you are using the proper type. They make files from the Factory that only have teeth on the wide side and NOT the narrow side precisely for this reason. If you don't own one or are unwilling to buy one (they are cheap) then yes I suppose one could grind off the side teeth, but just wanted to make you aware that there are files made this way.

Any time you are trying to do very fine file work you can see where you
are removing metal by frequently darkening the filed surface with an
ink marker. This really helps avoid angled surfaces where you don't
want one.

I say this as a sinner, not a saint: if you have to ask, it's probably going to look like a crack addict did it.

Any good gunsmith, machinist or metalworker will be able to do this quickly and cheaply and it will look professional.