This is a difficult question and needs parameters. Pretty much anyone before, maybe, the late 90's came from somewhere else, and lots were big names there. So if you're going to do that, it has to be Hogan. Though I don't really know how big he was outside of WWE. Beyond that, you would have to pick Ric Flair. He was and probably will always be known as the NWA/WCW guy.
From the late 90's to early 00's you had the ECW and WCW crowd, almost all of which have gone on to WWE. Out of that crowd, Chris Jericho is probably the biggest. Unless you argue that Austin was big enough outside of WWE. Actually, Austin probably was more successful than Jericho in WCW but I think Jericho was more successful other places maybe. If that's it, you have to give it to Austin then.
Now, if we're doing the post territory, post-WCW/ECW era, that limits who it can be. Because again, almost everyone wrestled somewhere else. CM Punk probably was on his way to being that guy. Daniel Bryan is probably more well know, but same thing as Pun, was an indie and ROH guy. AJ on the other hand was a guy on TV for more than a decade with TNA, and then also ROH and NJPW. So out of the current crop, he probably is the most "non-WWE" guy currently. But even then, his current success is still not huge.
So for me, based on someone being "known" as a non-WWE guy first, I'd probably give it to Ric Flair.