I've been giving the stick a slight wobble when he moves to bite, and it's been working.
Boo has something I call his "alarm" noise. It's kind of an urgent growl. He makes it when he sees a crow (he hates crows), or if something startles him. He also makes it if he's stepped onto my hand and my hand wiggles for any reason, making him feel unsure of his perch. I try to keep my hand as steady as I possibly can between his cage and my shoulder.
The perch shake would definitely distract him from biting - and I understand not wanting to get bitten. The one time Boo bit me wasn't one of my best memories of our time together. I'm just wondering if there might be something else that could work. The volunteer at the rescue where I got Boo had to bring him out of his cage on a perch stick, and as soon as he was on it, he went for her hand to bite her. She just waited until he was almost there - the perch stick was about 3 feet long - grabbed the other end of the stick and rotated it around, so she was on the opposite end of the stick from him. He went back for her hand, and she rotated it again. She did this as she got him moved to a perch stand, where she could put him down. It worked for her, and she didn't get bitten.
He liked men better than women, so it was easier for me. I just talked to him until his eyes stopped pinning, and he wasn't flaring his tail. Then I rested my fingers on his perch stand, but as far away from him as I could get, and I kept talking to him. He glared at my fingers, and lunged at them, but he didn't move to bite me. When he settled down and stopped glaring at my fingers, I moved them a little closer. We kept this up for almost an hour, until my fingers were right next to his feet. He lunged at me again, but I didn't jerk my hand back or do anything else to startle him. When he let me touch his toes, that's when he lifted a leg up to be picked up. He was happy and comfortable on my shoulder, and he didn't bite me until I was trying to get him off and put him back down on the perch stand. I got too aggressive and was chasing him around my shoulders with my hand. He just tried to avoid me until i pushed him too far, and he bit me good. I bled for a while.
I've since read that I also should have approached him with my head turned, and looking at him out of the corners of my eyes. In the wild, the only thing that looks head-on at a parrot and stares is a predator. Their instinct is to flight or flee when something does that. I've tried that on parrots in other places, and they seem more relaxed around me. Maybe it wouldn't have taken an hour for him to adjust to me if I'd done that.
Edited to add: I still can't put my hand up to my shoulder to get him down - he won't tolerate it. Instead I just move close to his perch, so he can step over himself. He knows when I'm leaning in next to his perch, that's his cue to climb off.