Owen would have probably ended up in WCW to join with his brother, Bret. I know Bret tried a few times to get Owen, but he was in the middle of a five year contract with the then WWF. If this contract had expired before late 2000, I think Owen would have jumped ship.
After the WWF takeover of WCW, I imagine Owen would have waited out his (no doubt lucrative) Time Warner contract and would have either retired or had a short run in WWE around 2004/2005.
As for wrestling itself. Sadly, I can only imagine that stunts would get more and more crazy until someone else died in a horriffic accident like Owen's.