After firing, I break the gun, pop out the hulls, sweep the heal of my off hand down the hammers as I reach for the shotgun belt. Very quick. Not world record quick, but much faster than what you describe.
A caviat. If we are talking about an un-modified TTN/Cimarron here, you'll slice the heal of your hand to ribbons on those little decorative horns. Take. The. Horns. OFF!! Don't ask me how I know this
Coffinmaker