Correct me if I'm wrong, but I think the team that claims him would have to keep him the rest of the season (barring a trade which is a bit complicated too). I don't think you can waive him again even if it's preseason.
I hereby correct you. Of course you can waive him again. I can't even remember where your version came in... it might have been back when there was a "waiver draft" a loooong time ago at the start of the season? I even had that kind of wording in my keeper FHL at one point IIRC. So I do believe it was a thing at some point in our past history of NHL nerddom, but I am not going to try to look it up!
So you can disbelieve me if you want!
But nowadays, you can claim and re-waive to your heart's content.
I think in a case like Ty Smith's... it's actually kind of an option that you could claim him now... re-waive him on the final day of camp cuts... and nobody else in the league would take him, because hey, a 2nd team just waived him, plus there are EVEN MORE interesting players available on waivers at the final cut. Then you might even get to keep him in the minors. If nobody else had wanted him in the first place.
But I will just also add that this is all "fantasy GM-speak". I am all-in on being a fantasy GM. But in the real world, with real people... I mean, our organization has just gone through camps with guys, the guys are stoked, the team spirit is there, the concept of jobs opening up is there for guys who didn't it make it this time around, everything is a very organically team-focused environment. I don't think you kick all that to the curb just because some guy who is kind of busting got waived on Day 1 by some other team. You don't push that guy to the front of the line ahead of guys you've been building that organizational repoire with. So I still can't see the Preds going this route with Smith, not in the real world. Or they'd have to have some super-positive pro scouting report on him, anyway.