My sister had Tetras with her Betta, and they weren't nippy as far as we could tell. She thought they were, but I think the Betta's fin loss was due to poor water quality. If you do choose Tetras just keep an eye on them to make sure they're not nipping.
Also when you're adding tank mates with Bettas it's a good idea to take the Betta out, move things around, then add the tank mates, and the Betta back in. That way the Betta won't recognize the tank as it's territory, and will be less aggressive towards any tank mates.