My IRN doesn't mind my right hand, hates my left though I realised today haha. Did some thinking and I realised I hold her with my left when I clip her nails and she hates being held so it makes sense. gonna do some desensitise training with her to see if that helps.
Do your birds have any treats they would ignore a pouncing cat for? try offering them and leaving the hand there while they nibble away for a bit? that's how I work with Lucky.