If you can figure out a way to plug the .22 mag barrel without ruining your firearm that would work. Also, make sure if you're going to hunt on state land with it only have 20 ga ammo with you. That helps to show your intent is to use the 20 ga and not the .22 mag.

Unfortunately the way the regulation is worded you couldn't use a .22lr in the .22 mag firearm, even though it will work. The regulation is specific regarding the firearm not the ammunition.

26-66-2. State-owned, state-leased and permit-required hunting areas; weapons
(a) Any rifle or handgun using centerfire ammunition may not be used to hunt on state-owned land. Any rifle or handgun that uses rim fire ammuntion having a cartridge case longer than that of a .22 long rifle catridge case and the projectile of which is heavier than 20 grains, muzzleloading rifles larger than .36 caliber or using any projectile other than round ball, crossbows and shotgun ammunition of loads larger or heavier than number two shot shall not be possessed or used for the purposes of hunting as defined in section 26-1 of the Connecticut General Statutes on any state-owned land, including state forests. This provision shall not apply to rifles possessed by persons transporting legally killed and properly tagged deer taken on private lands to check stations located on state-owned properties, approved rifle range areas or deer hunting with shotgun or muzzleloader during the open season on such land. Waterfowlers hunting from a boat, blind or stationary position may only use the ammunition specified section 26-66-4(t) of the Regulations of Connecticut State Agencies.

The firing pin on either barrel is easily removed by removing the screw that retains it. I believe that by removing the firing pin and not carrying the RF ammo that you would be OK.

I think being in possession of a 22 while deer hunting wouldn't be legal. I'd take his previous advice and plug it and leave the 22lr rounds home. Your not going to shoot many deer plucking squirrels all day anyways.