CoM is not always moving in exactly the same direction as the boots are pointing. For example during cross-over or cross under, CoM seems to the skier to be moving 90 degrees to the direction the boots are pointing; it's not actually 90 degrees, but it is far from zero degrees. During apex, perhaps the angle is zero (in an arced turn). It varies throughout the turn.
As to the direction a skier will travel after losing an edge, it is actually tangential, like the highschool pyhsics video releasing basketballs from a convertible on curve, but to the skier it seems to be radial, because they are accustomed to the turning frame of reference, just like it would feel like you were going off radially from a fast moving merry-go-round.