I've only held and shot a double action Colt belonging to other folks a couple of times. So I can't help at all with how to tinker on them. However I can suggest that for cleaning and lubing that you make up a little batch of Ed's Red. Then you can soak or flush the guts of the gun through the various openings and when it drains and dries it will leave behind a light film of ATF. If you want to add in a touch more slippery stuff into the batch of ER you mix up put a dosh of some good synthetic oil such as Mobil1. Not much, about 2 to 4% by volume. Any more and it'll leave behind a sloppy mess.
With an old squeeze bottle you can suck up the ER from a container and squirt it into the gun over a drain tub of some sort. The wood grip scales being removed of course. And while wearing your protective nitrile gloves work the action with a thumb on the hammer to avoid the hammer hitting hard, it's a rimfire after all, and get the solvents and oils into all the sneaky spots. After it's well cleaned set it so it drains out the excess and the solvents can dry away. Usually this takes about an hour if you're doing it in a cool place. Some GENTLE heat can speed it up. Like a hair dryer on low set about a foot to foot and a half away.
Lots of smelly and flammable fumes with this so good ventilation is a must. But it sure is effective.
This is likely the best way to deal with it. From what I've read Colt double actions are fussy things to work on. So it's likely not worth tempting fate to take it apart if all it needs is a good cleaning. And the Ed's Red mix is excellent for cleaning spots you can't reach. A quick trip to the local hardware store for the acetone and odorless lamp kerosene and Varsol or low odor paint thinner and then a stop at Cambodian Tire for a bottle of ATF and you're ready. I find that a liter size batch works for quite a few guns worth of cleaning. It still works even when it's quite black.
To dispose of the old stuff include it with any waste oil and return for recycling.
CONTENTS: Ed's Red Bore Cleaner
1 part GM spec ATF (Automatic Transmission Fluid), This is the red stuff.
1 part Kerosene - deodorized
1 part Mineral Spirits, low odor paint thinner or Varsol (the proper mineral spirits will dry away a little faster)
1 part Acetone