In general, fin nippers wont bother cory's they would bother slow moving fish with long thread fins like angels, and gouramis. And for what it's worth I think you would be fine to house several cory's in a 10 they really don't usually exceed 2 inches and are usually smaller in my experience. I think the pygmy variety are cool and would allow you to have more but you should be fine with the easy to find variety.
I also think that barbs tend to be nippier than any tetras I have seen. Most tetras would be fine.