I have a 1-gang box that I'm installing a switch in, for my wood shop. I need to make it dust-resistant, if not absolutely dustproof. I can't use a waterproof box because I don't think they're made for the depth I need (3.5") to fit the switch. Do they sell covers for the screw holes of j boxes, like they sell knockout covers? If so, what are these things called? If not, what are some other possible approaches?
Use a weatherproof box and a weatherproof extension ring (or rings if you need a lot of depth) if you cannot find a weatherproof box to suit.
Or, just seal up the box with duct seal (non-hardening electrical putty for sealing up conduits.)
Unless you use a weatherproof switch enclosure (which may not be compatible with whatever absurdly deep switch you have chosen if it's not like a normal toggle switch at the mounting end) the switch itself will be an entry for dust into exactly the places you most don't want it.
Depending on the nature/purpose of the switch, enclosing the entire switch behind a gasketed door might be appropriate - but not if it's something that requires immediate access, like an emergency stop (though most of those are dust-resistant and/or waterproof, or available that way, anyhow.)
Addressing dust collection/control is another approach. It's not good to breathe that stuff, so getting it out of the air ASAP is good for you AND your electrical items.
Look for switch/outlet insulators, like this one (Note: just the first one I found in a search, no recommendation of vendor or retailer implied.)
It's a thin foam gasket designed to go under the cover plate to keep cold air from coming in through the box, but should do a reasonably good job of keeping much larger dust particles from getting into the box, too.
Also, they're dirt cheap. (I found one source for receptacle gaskets for 10¢ each.)
In the US, NEMA (the National Electrical Manufacturers Association) is the standards body which establishes standards for this type of thing.
It looks like you want a NEMA type 5 box: Wikipedia Article on NEMA Enclosure Types