Looking at CapFriendly's simulator, we don't have all that many options at the moment. Under the rules we must leave 2 out of Couture, Kane, Labanc, Meier, and Hertl exposed. We must leave either Simek or Burns exposed. And we must leave either Jones or Korenar exposed.
I don't see Seattle having any interest in helping us out in the expansion draft either.
If we expose Jones, Burns, Couture and Labanc, then we force Seattle to decide to either take Labanc or a flyer on a younger guy like Gambrell (say, if he's not protected). I can't imagine there is a GM anywhere who has any interest in Jones, and I don't think Seattle would be very interested in Couture or Burns given their contracts, term, age, and (for Couture) injury history.
PS: The curveball in all this is whether there is another team that likes someone we leave exposed. Seattle could nab an exposed Shark solely to trade that player/contract to a third party for some other package. So someone out there might really be high on, say, Christian Jaros and be willing to work a side deal to trade a prospect and/or draft pick to Seattle in exchange.