Sometimes thought it is a bummer living in the states, less of an opportunity to go find some 1000+ year old relics knowing full well the likelihood of that happening is slim even if I lived in another country with bronze/iron age.
For an amateur but no less correct source, wikipedia provides a good quip for us:
https://en.wikipedia.org/wiki/Metallurgy_in_pre-Columbian_Am...
Archaeological evidence has not revealed metal smelting or alloying of metals by pre-Columbian native peoples north of the Rio Grande; however, they did use native copper extensively.[32]
Which then further cites: George Rapp Jr, Guy Gibbon & Kenneth Ames (1998). Archaeology of Prehistoric Native America: an Encyclopedia. New York: Taylor & Francis. p. 26.
I do not own this book, so I apologize I cannot verify the citation.
Keep in mind that you have to be wary of poisonous fumes - hopefully the elements giving their copper alloy a brassy appearance don't include lead, or worse, arsenic.
Moreover, purification from ores was done. The so-called copper bells of the southwest were mainly produced from ores rather than native copper and were often alloyed with arsenic or silver to modify the color. The main center of production was paquimé (~180mi west of the Rio Grande), but the cultural area extends well over the border into AZ, NM, and CO.
For particular lithics industries/tools and certain situations you might get some amount of reworking, but ultimately people were producing new tools very frequently. That means that any area in which you might find them on the surface will usually have some and a long term production site will have overwhelming artifact density. They can occasionally look like normal rocks, but once you train your eye the worked faces become visually distinct.
The "old world" had quite a head-start in digging up stuff and is also much more densely populated, so more people have been digging up old stuff for longer.