I feel like Shaw's animosity towards Picard for what happened at Wolf 359 is way overblown by people. Again, it happened twice. Once in a private dinner, and again on the verge of thinking everyone was gonna die. Both times Shaw was either drinking or on pain meds, so if anything, he needs to steer clear of drugs. His biggest hangup with Picard is his reckless endangerment of Shaw's ship and crew. Picard wouldn't have stood for it in his prime, neither Kirk or Sisko if someone came onboard with a secret agenda of their own that nearly destroyed their ships.
Yeah, Shaw is uptight and doesn't want to take risks. People like that exist in life, and dare I say needed, even when exploring space. Between the Borg and Dominion War, Shaw's content to run standard missions, a reprieve from the hell he, and many in Starfleet, have gone through.
If Shaw did get his own show, or became a Lorca-like secondary lead, then I'd expect him being tested with more adventurous missions, and dealing with his PTSD through Seven of Nine would be a major part of it. Character evolution, it's fun.