A polarizer can help tame reflections, and should not change the colors in the photo (except so far as they become richer and more saturated, which is the point of a polarizer.) The problem you will find is that when shooting shiny reflective objects, you are actually shooting the reflection, not the object -- it's the reflection that defines its shape and tone. So eliminating the reflection may cause the shiny bits to disappear completely, or just look odd.
You might experiment with very large light sources, like a light tent, that will show a smooth reflection over the entire shiny surface. Of course, that's easier with small objects than large artworks.