Skis will be as broken in as much as the can be after a run or two, as the only thing that breaks in is the fiberglass and/ or carbon. Wood is going to maintain its shape, as is any metal in the ski (though I doubt you K2s have metal in them)
And to that end, it's really the skier that needs to get broken in. I.E.- getting used to the new skis and getting back on the snow in the early season