Cotton cleaning pellets???

You don't have to remove the moderator. Just forget the cotton pellets and use a pull through with a patch. Put a straw down through the silencer for the string to go through so it never touches the silencer baffles. It also protects the crown not that weedwacker line tears up a crown. 

Works the same for shrouded barrels. Alan Z showed me that to clean shrouded barrels many moons ago. You might have to jab it a couple of times to hit the straw depending on how your baffle system is set up. Many moderators nowadays sold in the US are loctite'd on and a bear to remove. 

Don't ever use those felt pellets in a spring air gun. By themselves they don't provide enough resistance to the piston. No pressure in the barrel so the piston slams into the breach end of the cylinder. Not good.
 
Shot them out of my Commander in .22 all the time with a Koi sized at .25. Never had a baffle strike.

Currently shoot two out of my Concept Lite every time after 500 rounds or a tin of CPDs with a Sumo in .25. Never had a baffle strike.

I am using the Gamo felt pellets in .22. Watch out they go super-sonic and are NOT backyard friendly. They sound like I'm shooting off a .22 LR out of a pistol. There is absolutely a very loud crack and it sounds like I'm shooting a rifle. If you're in a backyard-friendly required environment I suspect your neighbors may think you're shooting off a powder burner.

If you shoot it inside be advised at short distances it WILL penetrate objects. Shooting the felt pellets outdoors they usually stop at about 20-30 yards due to air resistance.

Hope this helps! Like many topics some may agree and disagree and I absolutely respect their opinion and experience but I only use the felt pellets and my barrel is like looking down a mirror/kaleidoscope; there are no deposits requiring a patch/patch worm cleaning.

I find that after a patch and clean barrel it takes about 10 rounds or so to re-lead the barrel and get POI consistent.