"Should" be whatever you like in a Civil War period revolver. Some like the "factory new" blued look, some like the patina of time that the originals have become. It's really a personal choice thing. What do you want the gun to look like, a real antique that earned it's living and has fascinating stories to tell, or a shiny new museum piece lovingly kept free from harsh environments, ready to go to war at a moments notice?
Either is acceptable, both are done. I personally like my revolvers blued and my single shot pistols browned. I have no idea why. And nobody has complained or told me I'm wrong.