WP:Copper toxicity#EPA cancer data:
The EPA lists no evidence for human cancer incidence connected with copper, and lists animal evidence linking copper to cancer as "inadequate".
There is no information I could find on brass being considered carcinogenic.
Brass fittings are sometimes coated with cadmium.
Cadmium is itself toxic and many compounds including cadmium are known carcinogens. Cadmium can also cause developmental problems in children. In general, exposure to cadmium should be minimized.
I found no information on guitar picks being coated with cadmium, and would consider it unlikely in any case, as guitar picks (even brass ones) are designed with a limited life span in mind due to abrasion, so a surface cover to avoid long-term corrosion would not be effective.
When adding "Van Halen" to the search keywords...
Unlikely. The U.S. Centers for Disease Control and Prevention (CDC) and Environmental Protection Agency (EPA) do not classify copper or the metals in brass (an alloy comprised of copper and zinc) as carcinogenic to humans.
Van Halen has been a life-long smoker; it is "funny" that he should be looking for causes in sound studio's EM fields or metal picks instead of his smoking habit, which is well-known and -documented to cause cancer in all parts of the respiratory system including the tongue.