From my own experiences with mild TOS .. I would not focus on any arm repetitive motion exercises.. Exercise will increase blood flow in the compromised areas...Unless a very mild slow pace is used..

Full body gentle stretching, posture work & awareness, walking or exercise bike with arms neutral..
But expert PT or expert chiro can better evaluate you and what might be best for you.. The TOS drs should have lists of TOS experienced PTs..
The wrong exercises can make you worse..

Do you know if your top ribs are down/normal place, normal sized?
Are your scalene's in constant spasms or normal?
Also there's another bone that can be over sized and create issues..I can't recall the name of it right now..