Yandle is probably the prized possession now that Dustin Byfuglien has been signed to a long term contract. I believe it will take a fair amount to get him as the Rangers are still in the hunt for the playoffs. The real problem for them arises from his impending UFA status. The cupboard is pretty bare for the Rangers and they would definitely like to reload the prospect pipeline. Half of his contract is being retained by the Coyotes as well, so his cap hit is pretty lean. Even though the asking price could be high, Yandle could be a piece that takes a team over the top.
The problem for a player like Yandle, though, is his inability to suppress shots. Offensively the Sharks are set but maybe he adds enough on that front to offset any weakness.
If the Sharks are going to be looking on the defensive side of things, as far as rentals go, Coburn would not be a bad pickup. He will be a UFA after this season and already has experience in the Stanley Cup playing for the Flyers and Lightning. While he isn't a world beater offensively, the value really comes from his ability to suppress shots. This is an area of weakness for the team and he would immediately help in the short term. This could be a savvy under the radar move that Sharks fans should love.
Probably the biggest long shot on this list, Tyutin has been seeing third pairing minutes on the lowly Blue Jackets, but in those minutes he has been quietly excelling. His CF% may only be 51% this year but relative to the team he is at career best 4.16 CF%Rel. He has almost no value offensively but that is mostly due to his usage with the Blue Jackets. He does have two more years on his contract after this year but the Jackets will be desperate to move him, meaning retention of salary is very likely. While an outside the box move, he could be useful for the Sharks.