Final Verdict: I'm gonna have to say no here
It really comes down to this for me. Why would you take on that money, even if the Twins are paying half of it, for one year of Kepler and 1/2 years of Polanco (based on his club option), when you could just sign someone and keep Woo? That's the bugaboo, here, for me.
Couldn't you just give $10-12M to one of the hitters in that range, maybe up to $15M since that isn't a huge difference in the grand scheme of things in baseball, and still keep Woo? Then, if you are really looking for another hitter, you could just go and trade a prospect, likely one with a decent value (Gabby Gonzales, maybe?) for a hitter?
You'd end up still trading someone away with value, but your rotation stays intact, the payroll does grow a bit more, but you are in such a better position that the amount of incoming money from fans and tickets would easily offset the amount spent.
If there is really nothing else that is possible to do, and this is the only thing out there to make your team better... I still don't know that I move Woo for them. I need more. With how pitchers are going, it just seems like they have more value than this. Sorry, but I have to say no here.