Stahlberg isn't a 4th line guy - (he also isn't a top 6 guy unless you have a free slot for a development project -which I don't think Chicago has with Kane, Toews, Sharp, Hossa, a hyopothetical 2nd line centre and probably Frolik.
That makes him a 3rd line winger - 4th line being for dedicated checkers and defencive forwards (which Stalberg isn't - unless you want to convert him to that ... for the price of 4th line defencive forwards, that doesn't seem like a sound idea to try to convert a guy who is probably going to get more money than what a 4th liner ought to be getting.
That being said, I'd make him a qualifying offer to preserve any sort of compensation that an RFA signing elsewhere would bring, but I don't really see him having a slot at the expense of say, Smith, or Krueger, or any of the other guys out there -who knows, maybe Beach might be ready this season (although if there is any question of that - I would consider dealing the guy (Beach) in a package).
But Stalberg should definitely material for the trade block.