Not all tetras are nippy. Serpaes, black skirts, red-eye, penguins and bloodfins are the ones likely to nip but there are exceptions that can be applied. Rummy-nose are fine but they would actually prefer a longer tank to roam around.If it were me, I wouldn't trust a betta with any tetra. So I would go with a dwarf gourami. The cories work with both.
EDIT: and by 'trust a betta' I mean trust that his finnage would be ok