The normal method of attaching a Cutts to a shotgun barrel was to turn down the end of the barrel, then silver solder the compensator base onto the barrel. The screw was put back in place but not really needed.
Also, the barrel was cut back enough to remove any existing choke, since that would interfere with the intent in using the adjustable Cutts. If you remove the compensator, you will likely wind up with the cut and turned barrel and no choke. You could then have a gunsmith cut a "jug choke" back in the barrel, but a better move would be to have the bore threaded for internal choke tubes. You will also need to drill a hole to replace the front sight, since the Cutts has its own sight.
If you do decide to remove the Cutts (and frankly if you want a hunting gun, I would leave it for a while before deciding), you might be as well to just cut the barrel behind the comp. If you do decide to remove the comp, and it is soldered on, use a heat control paste to avoid removing the finish from the rest of the barrel.
Any way you "Cutt" it (sorry, I couldn't resist), that Model 12 is no longer a collectors' item, so if you bought it for that purpose you will probably not like the above. Sometimes you can find a factory Model 12 barrel, but they are scarce and expensive.
Jim