As Healthgirl implied, chronic use of Zn-rich dental products can lead to Cu deficiency though my understanding is that this is rare.

Blanewt, you could talk with your health care team about this. If your Cu levels are abnormally low then Cu supplementation might be indicated.

These links might help you with this.

Denture fixative cream and the potential for neuropathy. - PubMed - NCBI
Zinc requirements and the risks and benefits of zinc supplementation. - PubMed - NCBI
Denture cream: an unusual source of excess zinc, leading to hypocupremia and neurologic disease. - PubMed - NCBI