antiqueguy: There are entire cowboy action categories dedicated to keeping the sport as historically accurate as possible.
By far the best way to explore those categories that may interest you, such as: Plainsman, Frontier Cartridge, Classic Cowboy, etc., starts with a visit to the Single Action Shooting Society (SASS, for short) website.
Once there, pull up the Shooters Handbook, for complete descriptions of guns, calibers, costuming, rules and other aspects of these "Classic" and other, categories.
The guns you'd like to use would be perfectly suited in these roles. Including your Norinco hammer coach gun. ** You're part way there, already.
Shooting in these categories is a hoot and a half. As Plainsman and Frontier Cartridge for example, stipulate that only black powder (or bp subs) can be used as a propellant. Lots of flame, smoke and action.
Here's a great cowboy action source, on you tube: jeditv. Well worth watching.
Host "Jed I Knight", shoots exclusively in either Plainsman, or Frontier Cartridge (Gun Fighter) category.
The videos are shot at actual cowboy action matches. Including competitors (especially Jed) in action, full descriptions of stage instructions, etc. About the closest thing to actually being there.
So if this is the type of cowboy action you'd like to do, I highly recommend watching Jed's channel.
Al
ps: I'm with Cold Lake Kid. The 1860 is a fun rifle to shoot. Only problem is...that unprotected barrel gets hot, when shooting black powder. Still, I know competitors who like and use them. Plus, they are very historically correct and just plain cool to handle and shoot. So never a wrong choice. Just be aware of the rifle's limitations. A better choice: 1866. Arguably the most beautiful of all lever action rifles from the Wild West era. Plus, a joy to handle and shoot.
** Edit: Old303 is correct. Your 12" barreled shotgun would be disallowed at SASS sanctioned matches, due to barrel length. Many club level shoots are pretty informal, though. Ask the Posse Marshall in advance of a match, for permission. In the meantime, consult the Shooters Handbook, for detailed information on guns and gear, etc