if it's dry, you are fine (unless is it that crazy perfumey kind, but that has more to do with the lingering scent--by that, I mean "cucumber melon, ocean breeze, fresh linen" etc.).I know it all smells, but some have a ton of perfume that stays on your hands even after washing). I would suggest washing hands after use in the future--before touching the bird if you can (mostly if you plan to touch feathers a lot etc), but don't worry about it. You are fine. I should be a spokesperson for hand-sanitizer, given the amount I use. I have definitely touched Noodles with dry hand sanitizer on.
It does leave a residue, so if you have it on and haven't washed, I wouldn't touch their wet food or their water, because it could wash off into wet stuff...But I bathe in the stuff all day at work and have had to apply it in the car with Noodles and she has survived.
I wouldn't apply it in close quarters with your bird if you can help it (because of the alcohol) BUT, like I said, in a pinch, I have used it in the car with Noodles and just opened the window. I've had to do it on pretty much every trip we have taken, so that's over 50.