Keep whichever 4 of the 7 you cant trade!! .... seriously you should have no problem getting some sort of return for 3 of those young stud D-men.
Anyways the 4 I would keep would be
Karlsson
Fowler
Shattenkirk
Subban
that leaves out Hedman, EJ and Carlson ..... no i know there will lots of differing opinions on this one but I left off Carlson due to his "apparent" shift to more of a shutdown Dmen with offensive upside rather than an offensive Dmen who can play in his own end, I also think that Orlov could take some offensive minutes in the near future with him being a L handed shot (where Green, Carlson and Wideman are all Righties). EJ Ive never been a huge fan of, his is a solid all around Dman I just dont see the offensive upside in him that I see in the others. Finally Hedman .... he is the one I struggled with as I think he could be awesome he is just taking a while to develop but again I think he may not have the offensive upside of the others, having said that he is the one that I think could make you regret leaving him off he plays on a gifted offensive team and has a coach that could do wonders for his progression. Very tough call and you are in an enviable position having to choose from those guys but you cant really go all that wrong .... I think in any given season they could all be within 10-12 points of each other. I do think that Fowler and Karlsson are givens its the other two that are up for debate.