Yes, you can OC a shotgun. I'd make sure it stays on a shoulder sling to avoid any possible disorderly conduct charges.
The Cortez municipal code regarding disorderly conduct reads, "Not being a peace officer, displays a deadly weapon, displays any article used or fashioned in a manner to cause a person to reasonably believe that the article is a deadly weapon, or represents verbally or otherwise that he or she is armed with a deadly weapon in a public place in a manner calculated to alarm." Simply carrying a shotgun in one's hand (i.e. not on a sling or any type of holster) could be seen as causing alarm. If you stay on private property then the disorderly conduct problem goes away because you are no longer in a "public place."