Smiley sez...!
Remember, kids, a .22 LR of any type will suffer from too much bore scrubbing! Some gun writer for one of the major magazines (can't remember which, of course) did some digging and discovered that .22 accuracy delined with more frquent cleaning.
I used to clean all of my guns everytime I shot them about five minutes after I hit the house. Nowadays, unless I'm shooting something known to be corrosive, I run a properly "lubed" boresnake through the barrel a couple of times (which is a far cry from an actual, proper cleaning,) give the action a quick blast or two with a aerosol cleaner (sometimes as simple as WD-40,) re-oil/grease the running surfaces, and wipe it all down with an old hand towel. This goes for all my handguns, centerfire and rimfire alike.
My Ruger .22s, in particular, only get broken apart for a true-and-proper toothbrush-and-Q-tips scouring about every 500 rounds. The Mk.II 22/45 is running as flawlessly as it always has. And the Mk. III Hunter is singing along just fine now that I've removed the LCI.
When you do strip your Mk. III -- as others have pointed out before me -- remember to correctly orient that hammer tang, and that in order to do that, you sometimes have to pull the trigger, and in order to do THAT, you have to insert the (EMPTY!) magazine... unless you remove the magazine disconnect.