Lost in the Crawford / Darling conversation is that Darling is a UFA. There is no point in protecting him unless he signs an extension before the E.D. My guess is that the Hawks will try to reach a tentative agreement with Darling on an extension but wait until after the E.D. to have him sign it. They can then focus on whether or not it makes sense to try to trade Crawford. According to CapFriendly he only has a modified NTC, so there very well may be a number of teams they can trade him to without his permission.
It has never been released, but I'd guess it is a list of 7-12 teams. However, even a 7 team no trade list is a big deal for a goalie. Half the league has a starter already and can only take on $6 mil in net if they send back a goalie making $4+ mil. Chicago can't really do that, so the field is already a lot more narrow than it is for a top 6 forward or top 4 D man.
For example, say Crawford has a 7 team no trade list. Put Vegas, Calgary, Vancouver, Buffalo, Philly, Carolina and Winnipeg on that list and you have included basically every team that could afford to take on Crawford without also moving a goalie making $4+ mil. Montreal, Boston, NJ, NYR, Washington, Pittsburgh, Columbus, Ottawa, LA, San Jose, Edmonton, Minnesota, and Nashville all have established goalies and clearly don't have interest in burning an asset for Crawford. Toronto, St Louis, Detroit, Tampa, and Anaheim have identified an early-mid 20s goalie as #1, given him an extension, and committed so it probably doesn't make sense for any of those teams to go after Crawford. Colorado, Florida, Dallas, Arizona, and the NY Islanders may be looking at Crawford as an upgrade, but they have big money tied up in goaltending already and would need to find a way to shed salary. That 7 team list excludes all the teams that would immediately make sense, so there is a very small market to work with and any trade needs to get creative with salary. Factor in the UFA class this year (Bishop, Elliott, maybe Darling, Miller, Bernier, Mason) and the availability of Fleury and it isn't exactly a seller's market for Chicago.
At the end of the day, I think it will be very difficult to get anything close to fair value for Crawford. Unless they truly believe that Darling is a better goalie than Crawford, I don't think the asset coming back is enough to entice them to give Darling the #1 job without a safety net. The cost to keep Darling and acquire an adequate safety net will likely be as much or similar to Crawford and a cheap backup, so I think their decision will need to come down to who they believe gives them a better chance of winning.
I'm really high on Darling and am in the camp that thinks Crawford is somewhere in the 8-15 range of starting goalies. I'd probably try to move Crawford if I can extend Darling, but I think Chicago management truly feels that Crawford is in the tier just below the league's elite.