There has been fairly good discussion about the use of copper for pins. I didn't look up the link but you should search that. The information was quite good.
I've thought about the same and bought copper rod at the hobby store (a little thicker). It's easy to work with.
One consideration brought up that stands out in my mind when I think about using it is that it is softer. This presents a couple issues. 1: It will possibly get loose easier if used as a pivot pin. Perhaps less likely as a wedge pin. 2: It is softer and rubbing against the harder steel will create more friction causing more wear of the tang hole and or pin. A harder metal for the pin reduces this wear.
These are considerations that the manufacturers of old most likely took into account, thus you will not often if ever see straight razors with hinge pins of copper.
But if these factors are understood, there may be room for copper pins in your design. I haven't ruled out its use and plan on using copper on at the very least wedge pins and accent pins. I love the look of copper and its nice to work with.
Hope this helps.