I kept Tiger Barb and Cardinal Tetra together last year in a small tank (before I knew better re: size tank for the barbs). The Tigers ignored the Cardinals. Tigers must get their reputation from somewhere though, so I think much is down to the individual's temperament and how they then integrate in a group.
I feel I've been lucky with mine. They fight with each other sometimes, less so these days, but there's no visible damage to any fins. It seems more like strength testing each other with lip-locking rather than actually nipping at each other, and they haven't bothered other fish either in their original tank or new (ish) bigger home.
I would have thought as long as there were enough Tigers that they're distracted by each other and enough Cardinals that they feel safe from what they may perceive as a threat, even though it may not actually be the case, then you should be okay.