I would (and did) just convert a regular 10/22 over to what you want instead of trying to find a ready-made suppressor friendly option. Pretty much all of the 10/22 barrel makers (Tac Sol, Whistlepig, PWS, Green Mountain... so on and so forth) offer threaded 10/22 barrels of widely varying lengths and materials. Alternatively, you can also ship a stock barrel to JP grips and machine, and have them cut it down and thread it for ~$60. or for ~$130 you can get the barrel threaded and your front sight moved back.
I use my suppressor on both a 10/22 (w/ PWS T3 barrel) and a CZ455, and while the bolt gun is quieter overall, the 10/22 is still plenty quiet. A good polymer buffer goes a long way towards eliminating some fo the 10/22 bolt clatter noise.