Just following on what from Jollysue says, salt is really only needed as a specific treatment, not as a permanent additive. In most cases, it's just a waste of money. Your danios, neons and whatnot couldn't care less about a teaspoon of salt per gallon (~ tablespoon per 5 gallons), and assuming you have a proper filter and do regular water changes, the beneficial effects of salt (reducing the toxicity of nitrite and nitrate) won't be manifest anyway.
On the other hand, short term use of salt can be very useful, either as baths (dipping freshwater fish for 1 to 20 minutes in seawater) or as an additive for curing things like whitespot. In the case of things like clown loaches, there's some evidence that using brackish water cures them more safely than using copper-based medications.
Salt doesn't increase oxygen in the water; in fact it does the reverse: salty water holds less oxygen than pure water. What salt can sometimes do is provide a smaller difference between the salt concentration inside the fish and the water outside its body. (In effect, fish are "brackish" inside their bodies, so the more brackish freshwater becomes, the less salt is lost to the environment and the less water seeps in.) Under certain circumstances, this "support" can be helpful, in the same sort of way that salty drinks are helpful to people who have severe dehydration.
That said: most freshwater fish don't encounter salty water in their natural range, so there's no real advantage to keeping freshwater fish in water with tiny amounts of salt added. Some people do, but I doubt they're getting any benefit from it.
Anyway, getting back to the original point: I agree with Inchworm that basically any commonly traded Corydoras can be considered hardy provided you keep them in an aquarium with good water quality and water chemistry somewhere within their range of tolerances. Dr. David Sands (a Corydoras expert) has stated that Corydoras will tolerate small amounts of salt. I'd personally not expose them to more than SG 1.003 (that's about 6 grammes of salt per litre). Most hardy freshwater fish are not bothered by that amount of salt. Still, if I was looking for a catfish for a brackish water tank with mollies in, I'd be looking at Hoplosternum littorale. It's a relative of the Corydoras genus, but naturally inhabits brackish water (in preference to soft/acid water in fact) and will tolerate up to 40% normal seawater salinity.
Cheers, Neale