If Sir Patrick was let go, I think they would have tried to return to formula as quickly as possible.
Riker, as captain, would quickly get comfortable making "the big decisions" and accepting of the risks associated with them. He might be a somewhat less cerebral CO than Picard -- I doubt we'd see him quoting Shakespeare to Q -- but nonetheless would follow in his footsteps with conferences and discussions, and I'm sure we'd see him once or twice trying to read some of that high-brow literature that his mentor found so valuable.
I also think Shelby would remain onboard... mainly because promoting any of the regulars would mess with the formula a bit too much.
While it was cool seeing Data take charge in Redemption and smackdown Hobson, it wouldn't do much for the show overall to either remove their resident explorer of humanity or have a naive XO who constantly expresses childish wonder at the motivations of others.
And Riker's other choice of Worf would probably end up creating the same kind of redundancy that existed while Yar was still alive: two very aggressive "warriors" on the bridge, advocating for the same approaches, both eager to apply their skills. I'll grant that my opinion discounts Worf's ability to grow, but at this point in TNG's run, I don't think he was ready for command.
Shelby, on the other hand, is exactly how Riker was originally conceived. She's an ambitious risk-taker on her way up. She'd be the perfect foil to the newer, calmer Riker -- just as Riker was a foil to Picard (at least that was the intention). And while I think it'd be interesting to watch her push Riker in his new role, I would probably expect the producers to have him temper Shelby's energy. And by the end of the fourth season, we'd have Jonathan Frakes as Captain Jean-Luc Riker, and Elizabeth Dennehy as Commander William T. Shelby.
Formula: restored.