I don't see them taking Byram with their first pick. They can get a good Dman with their 2nd first rounder if they want and while Byram is really good, there isn't a massive gap between him and several of the others. The Kings need to generate some excitement with this pick after a bad season and there are some really elite forwards up there. Byram is a really good two-way Dman but he isn't Rasmus Dahlin and I don't see the need to go that high for him when there is a closer gap between the Defenseman in the first round than there is with the top Forwards and the next tier.
If they are not in the Top 2, then it will probably be a "who is there," when they pick. If Cozens is on the board, they are going to take him in my opinion. He is big, skates very well, has one of the best shots in the draft, plays a 200 foot game, has a great attitude and most important, he can play C or W. He seems to be an ideal complement to Vilardi(if he ever is healthy) or Kupari.
After Cozens, it is probably a tossup between Turcotte and Dach for the Kings with a slight edge to Dach because Turcotte played so few games. It think that it will be one of those 3 guys after the Top 2.