Ok you can do with electro plating, both terminals carbon, remove the copper regularly from the cathode, you wont get 100% removal though.
You can displace with Iron or Aluminium, but you get Ferrous Nitrate or Aluminium Nitrate. The other ways are a bit more involved chemically.....
Heat the copper nitrate so that NOx brown gas comes off, feed that into cold water, isnt as pure nitric acid but its fine to remove copper, or you can distil it. The your left with Copper Oxide, this you can return to copper by heating with Hydrogen atmosphere.
2 Cu (NO3)2 → 2 CuO + 4 NO2 + O2
3NO2 + H2O → 2HNO3 + NO
CuO + H2 → Cu + H2O
Removed the Carbon monoxide route because I hadnt given it as an option.
OR
You could mix the copper Oxide with hydrochloric acid to make Copper chloride, thats a fairly good etchant itself.
CuO + 2 HCl → CuCl2 + H2O
I would drop the Amps to ~1 if you use electrolysis and the Voltage under 5V, 4.8 ish is about right. Actually drop to 4V and 3 A should do it. But you need to keep removing the copper from the Cathode.