I think your basic strategy- trade Braun or CarGo- is sound, though see if you can package either with Holliday for a better pitcher than you could get in a 1:1 trade. If someone is pitcher-heavy and needs bats, Holliday is still a great option.
As for which one to deal, I'd put both out there and take the best deal you can get. Maybe go the "offer CarGo, settle for Braun" route. Braun is probably marginally better than CarGo, but if you have to deal him to get the guy you want, it's worth it in the end.