Assuming by tetra you are referring to the standard species, they will not bother corys.
Corydoras habrosus is a delicate species. When you were in my fish room a couple weeks ago, you probably saw my group of this species in the 70g. I do not have particularly good luck with them, nor with C. pygmaeus edither. Not sure why, as my many wild-caught species in the 115g do very well and are regularly spawning.
Charles (you know who I mean) told me that the dwarf species must be on sand, and I have had better luck since changing to sand. But I still have losses higher with these two species than anything else. Dr. Neale Monks wrote that the "dwarf" corys need lower temperatures, no higher than 75F max, and I am beginning to accept that this may be my problem. My tanks are 76-77F, and this may just burn the little corys out.
Byron.