CHI 2nd, Nate Davis + TOR 3rd or Pavel Vorobiev + CHI 4th, whichever Boston prefers.
I get Davis isn't playing this year, he's not some missing piece he's a contract throw-in so Chicago can make this deal happen.
Davis isn't playing this year, great, but his contract is still counting towards the 50 contract limit for the Hawks.
Boston gets the pick they're looking for in return for Stuart and Chicago gets their UFA Dman. Davis is just a throw in that has no effect on anything other then moving a contract.
Boston doesn't want a roster player in return for Stuart, but I don't think the Hawks want to give up a signed prospect either (Danis-Pepin, Connelly, Stanton etc.) so Davis, even though he's not playing, is the contract that goes the other way to make it work.