As IHeartPieds has said, you could try redirecting his attention in another way, also:
Perhaps stop watching the bird videos, or watch only briefly if that gets him overexcited.
Rethink how you actually play with him - remember that birds don’t play in the same way dogs do - Ask yourself, could you actually be teasing/frustrating him and he’s telling you in bird language “no, not like that!”
Birds like to test things with their beak, chew and pull things - consider, giving him something (other then your skin) to play with when on your shoulder - you could wear a homemade necklace of strung bird safe beads, wooden chew pieces, jiggling items and shredder toys, or pin a bird toy onto your shoulder epaulette style. I doubt you’ll start any new fashion trend but it might help you avoid a few nips.
You might also want to look up ‘gentle beak technique’