probably wouldn't hurt to cross post on something like this.
as long as you don't mind having the suppressor dedicated to the host i don't see a problem with an integrally suppressed 10/22.
and it'll look just like any other bull barreled 10/22 and not be obvious what it is until it doesn't make noise when everyone expects it to.
it will also be shorter than most other configurations.
from what i've heard, either getting the factory bolt modified by radiusing the rear surfaces where the hammer rides as the bolt recocks the hammer will help performance with subsonics. you could also get an aftermarket bolt. modified bolt will be about $50 or $60 and a new aftermarket bolt will me slightly more from Rimfire Tech, Kidd or Volquartsen. the last oe comes with their own charging handle design and the recoil spring and rod. the others will come without the changing handle recoil rod assembly and a good one is about $30 from many vendors.
and you'll probably want a nice trigger. upgrades to the stock trigger start at about $30 or $40 for just an aftermarket hammer and go up. complete trigger groups are about $200 from RT or VQ and the Kidd single stage is about that prie too, the Kidd two stage is a little more.
there are are several ways to lock the bolt, turning the rifle into a single shot but making it quieter. one replaces the guide rod and charging handle (this design won't work with the Volquartsen bolt), there's one that requires receiver mode IIRC and other DIY versions that are an aluminum plate cut to fit in the ejection port behind the CH and held in place with a rare earth magent.
i've heard good things about the Gemtech Oasis... that it's "spooky quiet"... much quieter than screw on cans.