My few cents:
If Shawn woulda legitly left WWF would be in a hard spot.. but to be honest I could see them eventually climbing their way out of it. Things would be different of course but it wouldn't have been the worst thing in the world if it had happened in 1997. 1996? Possibly. Shawn was their top dog in 1996 and the people decently loved him but things started changing by fall of 1996. They forced him down everyone's throats and the crowd started to turn. The In Your House vs Mankind had some smarks in the audience but Survivor Series was really the decline of his face movement. The crowd was sick of him and booed him out the Garden while cheering massively for Sid. That seriously hurt him and he never recovered from that. The fans wanted someone else desperately. RR 97 was an outlier because they had to do it in his hometown. Him winning the belt anywhere else woulda been backfired on. People were growing tired of his routine.
With him gone honestly no one woulda missed him I don't think on the product and definitely not backstage. It does hurt not to have a major face around but due to the fatigue I think the natural audience would be willing to overlook it. Internally in fact Bret would probably go down forever as the hero and would stay around. They'd have to find a way to redo his contract but I see Vince being more willing once things improve. As for who replaces HBK? Austin definitely becomes the top face by August, that was always destined. Bret still is the heel Canadian hero, and the Hart Foundation reunion still happens. Rock still turns heel and joins the Nation, Foley still has his promos with JR which turn him and feud with HHH. I think the big benefactor would be Ken Shamrock honestly. He was in the mix as a potential victor over Bret for the title once he let it be known that he wouldn't drop it to Shawn. I doubt he'd win it in this 1997 but I def see Bret requesting a title match with him, they'd do excellent together at an In Your House. Vader could also possibly get that face run he deserved and a title shot, Mankind as well. Patriot possibly as well if he could stay straight. A lot of potential for a more eclectic lineup once Taker drops the belt to Bret at SS 97. Only real thing we may lose is the first Hell in a Cell Match but honestly they could potentially put one of the HF guys in it and I see it working. Owen Hart in Shawn's spot would be fun. I could see him doing the table bump perhaps. He'd win it like in RL once Kane comes out. Bret would face Taker for the title at RR 98 and be his main feud until Austin wins the Rumble. Casket match happens but no back injury for Bret.
Mania 14 would happen and Austin would win, it was his destined time. Bret would lose clean then get knocked out by Tyson for added flavor, it would give Bret some needed time off while Austin feuds with Owen and Davey along with Foley and Kane. Bret would be gone for a bit then comes back for a reduced schedule but he'd be a face instead. WWF goes the same way as RL as the wildness comes in. Sable takes off much like in RL, Rock gets his push, Taker/Kane have their feud, Shamrock becomes either a tweener or top heel, and so on. Bret becomes a part time attraction while getting into movies and his hobbies. He'd retire by 2001 or 2002 much happier.
As for Shawn? He'd either come in as a face and ally to Sting or he'd be in the NWO as one of the Wolfpack with Hall/Nash and Syxx. If it's the former he'd be another face in what was once the best idea in a long time growing out of control. He'd probably take Curt Henning's spot but he in better shape. He and DDP would probably have a hell of a US Title match at Starrcade. Going forward he would go with Nash to join the red and black and they'd be a lot like DX in terms of being more wilder. Probably would be a lot different than the RL group. They'd be younger and more bold. No Savage/Luger/Sting. Konnan would stay but it would be younger guys and they'd be bold and take on the old black and white NWO. Eventually he'd either turn on Nash and join Hogan or would leave post finger poke and go on his own.
If he goes face he'd be the top WCW guy along with Sting, he'd kill off Luger's momentum in that way. He'd probably be what they were wanting Hart to be which was the pissed off outsider who wants to re-avenge the company and reverse what the outsiders did. If they go all the way through with it I could see the NWO ending by early 1998 perhaps. Hard to see happening with Hogan's pull though. Something would have to give there, especially if Bischoff screws up and gives Shawn the same pull Hulk had.
A big determiner of his destiny would be his issues; they'd get a lot harder if he doesn't hurt his back in WCW. With the lax nature of how they ran things there's a very good chance he either gets busted or OD's in this world. There's be nothing there to prevent him from either OD'ing or doing something stupid if he didn't get the help he needed. Granted his wife was there but there's no guarantee they'd hook up here. If they do he eventually does get straight and has a nice run to end on his feet before the company dies off. Does he go back to WWF? Possibly not, if Vince views him as a traitor like Savage he wouldn't consider it but who knows.