For cleaning purposes you do not need to remove the handguard.
Remove only the end-cap(which is held in place by 4 protrusions that clip into the end of the handguard) and slide it down to the flash hider, move it back when done.
Once the end-cap is moved from the end of the handguard, use a wooden dowel or cleaning rod covered with an oiled cloth to clean & oil the exterior of the barrel.
The barrel nut mentioned does indeed need to come off in order to remove the handguard and to remove the barrel, but neither are needed or recommended in order to properly clean this rifle. The barrel nut is not designed to be user removable therefore this step is not part of field stripping/cleaning. If it was, S&W would have used a different design for attaching the handguard and barrel. As mentioned, a barrel nut removal tool is sold. I would recommend that all 15-22 users get one of these because this barrel nut unfortunately has been known to come loose on some users. An occasional check or tightening is probably a good idea.
A true military issue AR rifle is designed so that the handguard can be easily removed so the exterior of the barrel can be cleaned, however the barrel is not designed to ever be removed by the user for any reason.
The 15-22 can be fitted with a replacement barrel nut which will get you started if you want to install an AR style handguard, either free-floating or captured on both ends. If you want to install a two piece handguard additional items are needed to secure the handguard at the upper receiver end (i.e. d-ring assembly) and at the muzzle end (i.e. gas block or front sight assembly).