In studies of Wilson's disease patients, 50 mg TID (3 times daily) Zinc Acetate is effective, no toxicology follow up was conducted however.
Zinc works by decreasing copper absorption.
Zinc and acetic acid have weak bonds that break, allowing plasma zinc ions to roam in the body. I'd take low dose zinc acetate at 10 - 15 mg x 3 daily with meals to inhibit copper absorption if I KNEW that copper was in excess roaming free.
Cysteine is a very good chelator of copper, including cobalt, ferrous iron, mercury, nickel and zinc. That would be good to take to actually chelate copper, especially if you're actually high in free copper.