OK - I was trying to find a manual for the Model 402 (or the 400, which is the rifle version of your carbine), but no luck.
Looking at a schematic of that gun, you are going to be very limited as to how well you can clean it.
What I do with similar rifles is to use a Bore Snake, or similar product, and Break-Free to clean the barrel and Break-Free to clean the other metal parts.
1. Put some Break-Free (also called CLP) just in front of the bristles of the Bore Snake.
2. Open up the action by pushing the lever down and then feed the Bore Snake through the ejection port, into the chamber of the barrel, let the Bore Snake cord drop down though the barrel, and then pull it all the way through when it appears at the muzzle.
3. Repeat steps 1 and 2 at least 3 times.
4. Take a Q-Tip with the tip soaked in Break-Free and swab the inside of the action by going through the ejection port. Then take a dry Q-Tip and wipe down the area to remove the CLP (a fine coat is always left behind to protect and lubricate the gun). If the dry Q-Tip is really dirty, repeat this step.
5. Finally, wipe down all the exposed metal parts with a patch soaked in Break-Free and then use a dry patch to wipe off those same parts.
6. When you are done with steps 1-5, your gun should be clean, lubricated, and protected. The lubrication should be almost undetectable so as to not attack dirt, dust, and lint. Further disassembly of the gun is also discouraged.
There is also no point in cleaning inside the magazine tube.
Keep the wood clean and dry.
I hope this helps.