Wild snappers can be docile. My avatar is the nicest snapper I've ever handled, wild or captive. Gloves help with claws and super strong legs.
From my experience with wild snappers, tiny ones are too timid to bite. Huge ones are too confident to bite. Juveniles to young adults (5''+ shells to 15lbers) are the most difficult to handle, and are the most likely to snap multiple times. The very few 20+lbers I have handled have been very reluctant to defend themselves, but their legs are difficult if they get squirmy. They seemed unconcerned with me holding them, and just seemed to try to swim away. Young'ns are the only ones I've seen prone to snort, snap, spin, and spaz out to try to scare you off.
My theory is that like many reptile species, they can grow out of any stereotypical nippy-ness, but they are all individuals. Keep in mind that it will take a snapper much longer to get to the "alpha predator in my environment" stage of life than various python species (for example). I'm not sure how much that regular handling can play a part, but I AM sure that being healthy and happy are a huge part of it, as with any captive reptile. An unhealthy reptile is more prone to being defensive.
Q to the OP:
How are you handling basking and his albinism? Any issues you know about or are experiencing?
Great looking animal, I'm super jealous. I may have to talk my girl into letting us get a snapper this year. I've got plans for a 7x12 indoor area we could convert for one that is up to size.