I think at this stage you are best to let nature takes its course. You can however plan ahead, as once Corydoras spawn they will be spawning again and again.
The eggs are the most vulnerable because they stick where the pair lay them. In a tank with fish, including the cories themselves, few will survive, as fish eggs are a high item on the menu of all freshwater fish. Eggs laid in "hidden" spots can survive, and hatch. The fry are better at surviving than the eggs because the fry can swim under cover. If you want fry, one important thing is to have dried leaves in the tank. These produce infusoria as they slowly (very slowly) decompose, which is the ideal first food of all fry. I have raised cory fry with just leaves, then adding Omega One shrimp pellets which are easy for the tiny fish to nibble on.
Uberhoust's advice was excellent for preventing fry being pulled into filters. In my former tank which was 70 gallons with an Eheim canister filter, that I cleaned every 2 to 3 months, I often found cory fry in the bottom of the filter. They got pulled in as fry (eggs are too sticky) and manged to live there for a few weeks. I netted them out and into my 20g QT tank for new fish which sat empty of fish most of the time, but was an established tank with sand, chunks of wood and thick floating plants. Dried leaves in here too, and the fry grew well. when large enough, they went back into the main tank.
The above works when you are not particularly desirous of raising dozens of fry. If you are, first thing is you must remove the eggs right after they are laid, or something is likely to eat them if there are fish. The cories themselves will eat them too. The eggs need to be very carefully removed from where they were laid and placed in a small tank of their own, sand substrate, plants, dried leaves. I once used a nylon fry net in the main tank, hanging from the tank frame in one corner. Dried leaves in here too.
