If you have an ultrasonic cleaner, that's as good as it gets and you need to do no disassembly.
If a US cleaner can clean tiny watch assemblies without disassembly, comparatively huge guns are easily done.
I suggest buying a gallon of cheap paint thinner.
Do this carefully since it is moderately flammable but not explosively so like lacquer thinner or Acetone.
Fill the ultrasonic tank, turn it on and let it run a while until the solution starts to heat up.
Warm solution cleans better.
If the tank has a heater use it, but don't get it too hot and risk a flash fire.
Allowing the tank to run also forces out air in the solution.
You can speed it up by putting the paint thinner in a sink of hot water to pre-warm it.
After the solution is warm put the gun in, using wire to hang them so they're not touching the bottom or sides of the tank. US works better with parts suspended in the solution.
Run about 20 minutes of so, then remove from the tank and flush by putting clean thinner in a pan or whatever you have that will allow submerging the gun and swishing it around.
While you can rinse by putting fresh thinner in the US tank and running it, this is not necessary since just flushing it works just as well.
Remove and shake or blow as dry as possible, then use a hair dryer to warm the parts until they are completely dry. This will take longer to get the cylinder assembly totally dry.
(NOTE: Hair dryer....NOT heat gun or torch).
Once completely dry spray thoroughly inside and out with a spray lubricant.
Operate the action and ejector to distribute the lube.
Shake or blow with compressed air to remove the excess, and it's done.
You can also do a good job with water and a liquid soap cleaner.
Be careful with the strong cleaners like Simply Green and others because most of them WILL attack aluminum and anodized parts and can ruin a part fast.
This will work well on normal fouling but not really well on rust.
After cleaning, swish in a sink of hot water and shake-blow dry, then use the hair dryer.
You can also use a water displacer like WD-40, then blow dry.
Note that ultrasonic cleaning will do little for leading and nothing for copper fouling unless the cleaning solution will attack copper.
Usually you'll still need to use a rod and brush to clean the bore and chambers, then use the ultrasonic cleaner.