Pet bird owners: cleaning question

Great.
I just let my parrot run around on the floor on the porch for a moment, so he directly tried to crawl under a cabinet-- of course this weekend apparently a bottle of bike chain oil was left open and knocked over and ran down the side of the cabinet so dear parrot got some of this stuff on his back feathers near the base of his neck-- I’m not sure if he can reach it to try to clean it but this is “modern” chain lubricant so I’d really rather he didn’t. How should I get this stuff off of his? Dr. Bronner’s peppermint castile soap? Dawn (they use it on oil-spilled ducks, don’t they?)? A parrot, unlike a duck, is not supposed to have oily goo on it. Suggestions?
God, I’m going to have to manhandle him and he’s going to take a chunk of of my hand. . .

Ugh. Ok, a couple of websites suggested citra-solv and then Dawn and then water. I’ll let everyone know how it goes, since I’ve gotten your attention. . .

Is there anything toxic in the chain oil? Can you check the Material Safety Data Sheet? If I were you, I’d want to make sure that I didn’t use a more toxic substance to remove a less toxic substance.

I also wouldn’t want to lose a chunk of hand for nothing. What kind of parrot is it?

Yeah, I think capy’s bird is a Jardine.

My kakariki got stuck on a strip of flypaper. After peeling him off, I cleaned the sticky feathers with Dawn and rinsed well. Voila! One angry, wet, but clean bird. He could preen to his heart’s content and I didn’t worry about him ingesting any sticky goo.

I bribed him out of his snit with a dried chili pepper.