I hope I don't come across in a bad way, but this is text and sometimes it's hard to convey emotion; so all I say is intended to help.
There is no guarantee that they will get along, even if your betta does not seem aggressive now. And even simply chasing tankmates with no physical damage can stress the other inhabitants enough to cause them to hide. I experienced this even in a larger tank (20g), with a dwarf gourami; a fish that should have been ok as long as he was the only one of his kind, but he was not; and I had to separate him from my cories. And his aggression took at least a month to manifest.
Corydoras are wonderful little fish, and probably my favorite. While they eat from the bottom; mine spend most of their time on all levels of their tank. They are whimsical and playful, and spend alot of time "dancing," frolicking, or courting each other in preparation of spawning. When they feel stressed they hide; and that is not normal for them. And when any fish is stressed, it is more likely it will become ill.
So I say this to you, that what you plan might work or might not. Just please do keep a close eye on all in the tank, so that your little cories can be as happy as your betta. :) And because sometimes territoriality or food aggression takes time to manifest; have a spare tank on hand that you can put your betta in if need be.
I wish you luck! Corydoras are delightful little creatures. I was unable to house a betta or even a gourami with fellow fishes; I always ended up with the ones that got snarky.