What tests could I use to prove that a solid product is copper?

Answer 1

Eureka!

Measure the volume of the displaced water (from dropping said object into a graduated cylinder of some sort), and knowing the mass of said object, compare to the density of pure copper.

...Just look up density and Archimedes online for more riveting details.
.....You could still use the molecular analysis if you want, but my way is faster, cheaper, and requires no specialized equipment beyond a container of water and a scale.

Answer 2

I doubt you have one at your disposal but if you happen to, an EDS (Electron dispersion spectroscopy) can do the test. it works on all elements by shooting a beam of electrons on the surface and based on how the beam is scattered the outcome can accurately determine what element and how much is present.