You are allowed to register ONE vehicle with a disabled plates, and be exempt from the weight fees. The other cars have to use the hang tag, or perhaps if your wife is also disabled, you can have a second car with handicap plates.
I registered my dune buggy with handicap plates, because it does not have a roof or doors, hanging the tag inside it might get stolen.
You should be able to change your truck at AAA, and I really see no reason to go into DMV.
You can look up some information at
https://www.dmv.ca.gov/portal/dmv/detail/pubs/brochures/fast_facts/ffvr07There is also a exception for 100% disabled veterans, if you qualify for that, then no need to pay any registration fees at all.
Also California Vets who have any disability (my buddy was 5% disabled due to having pneumonia when he was discharged) your kids can get a free ride at any California State University - they only need to pay for books and parking. .
Good luck!
Fred.