Not sure how much help I'm going to be here, so hopefully someone with more experience will chime in.
I have two green cheeks, both were hand-raised babies...but they're also my first birds, so I completely admit to being a noob with birds in general (though I have found Avian Avenue to be a very helpful forum for bird related questions, if it's okay to recommend other forums here...).
As for dealing with shyness around hands, can I ask how long you've had him/her? Their approximate age? And has this always been a problem. I will say, personality wise, my boy does NOT really care for pets/hands in general. If I'm asking for a step up, he much prefers to step up onto the back of my first (flat surface) versus my fingers. I'm not sure if it's because I tried to force interaction when he first came or if he's had bad experiences or if that's just his preference, but Brae just isn't an overly cuddly boy. He loves to sit on my shoulders/lap/keyboard and be *with* me, but he doesn't necessarily want to be petted. On the extremely rare occasions he might ask by putting his head under my hand, it might very well be with an ulterior motive of conning me out of the computer mouse.
On the other hand, my girl Honey, loves head scratches. She'll crawl right up on me, bend her head and scratch the side of her face with her foot and then pause and look at me, then do it again very slowly until I get the hint. EVEN then, depending on her mood she can go for days or weeks at a time if she's in a mood where she'd much rather not have me scratching around in her feathers. :-p Then she'll randomly be back in the mood and cant get enough of them. To me, Brae just seems to like his personal space and he prefer to be the one doing the preening (freckle removing on me, oww! and grooming on Honey) and I notice he doesn't often seek out preening from her...though will consent to it when she insists. Unless he's molting, he'd rather be chilling with me or exploring, rather than tolerating being petted. Honey on the other hand, all around prefers to cuddle. Against my neck, under my hair, seeking WAY more touching from both me and Brae. So it might just be your bird's personality?
You *might* try some beak rubs. Both of mine do like to have their beaks rubbed/scratched, though not all the time so you have to learn their body language, but with scratching the top beak you get a little control when they go to bite you and can keep yourself from losing skin.
I'd also keep in mind (though you might already know!), that anywhere other than the head is essentially a sexual place to touch a bird. So you can over stimulate them quite a bit by touching in other places.
