Bill Tindall, E.Tn.
This is not an easy question to answer. Traditionally nitrocellulose lacquer has been used to keep silver and brass bright. I suppose it would similarly keep copper bright. This thin polymer film is not a barrier to oxygen diffusion, yet it retards oxygen from reacting with brass or hydrogen sulfide from reacting with silver. I don't know how it works to keep these metals bright. Since I don't know how lacquer works I can't speculate whether a urethane varnish would be as effective. You can buy nitrocellulose lacquer in spay cans. I suggest using what has been shown to be effective for brass and silver.
The name "polyurethane" tell us the chemistry of how some components of the finishing product are chemically hooked together. The name does not offer a clue as to what is hooked together by "urethane" linkages, or what else is in the formulation that could affect it corrosion prevention. Some polyurethane varnish could be better or worse than lacquer, or a different polyurethane. No way to tell without testing.