It isn't absolutely necessary to remove the clean-out screw, many are not removable. My normal cleaning method for a half stock rifle is to pull the barrel, remove the nipple, stick the breech end into a bucket of warm soapy water and with a patch on the jag of the rod, pump water up and down through the bore. That will clean the drum between bore and nipple seat. You can then bend the end of a pipe cleaner and work it through the flash channel to get it clean and dry. Always remove the nipple, clean and dry it and give it a drop of grease before reinstalling. The clean-out screw is optional and if it doesn't come out easily it is better to leave it alone than to bugger it up.
I had one of the little Bobcats with the plastic stock and found that the pebble grain texture abraded my cheek even with only 50 grains behind a patched ball. It was reasonably accurate and nice to carry but not at all nice to shoot.