Corydoras can also get oxygen from the surface somewhat like a Betta in low dissolved oxygen water, however, it is swallowed and absorbed via the GI tract since they don't have a labyrinth organ like a Betta.
The bubble wand doesn't put oxygen into the water per se. As the bubbles hit the surface of the water it cause a gas exchange. Oxygen in and CO2 out and too much agitation at the surface can drive too much CO2 out that the plants need. And as you already know-the plants also produce oxygen as a byproduct to assist.
Since it is causing problems for your Betta-I would either remove it or use valve as Gizmothefreaky suggested.
How are the corydoras acting, have you seen them go to the top and gulp at the surface on occasion-if so, that is normal.