I will assume by starter fish you are referring to a new tank and putting in these fish to start the cycle. This is not safe for any fish. Corydoras are sensitive to ammonia. All fish are for that matter, and even if they live through "cycling" they almost always have a shorter lifespan due to the negative effects down the road.
There are two (some will say 3) methods of setting up a new tank that are safe.
One is using live plants. With sufficient plants, including some fast-growers like floating plants, you can put a few fish in and gradually increase the fish. The plants use the ammonia, so there is no rise in ammonia or nitrite to harm fish. The bacterial cycle still establishes as usually, but it will be slower and undetectable and the fish will not be affected.
Second is seeding the tank with bacteria, including a reliable bacterial supplement. Again, few fish and go slow.
Third is cycling with dead animals like shrimp. It will work (so others say) but not something i would ever do.
Be prepared to do 50% water changes daily if ammonia or nitrite rise above zero. This is unlikely to occur with the plant method (never has with me), but might with the other two.