well the wider tip does relate to the way the ski bends....so it can definitely effect things.
You are right that it doesn't matter if the tail is wider then the tip because as I said earlier...its the edged and bent ski that causes more lateral force on the front of the ski then the back. The wide tip and tail are what causes the ski to bend and of course actual shape of the bent ski will create different kinds of bent shapes which will react differently to the centripetal forces. A wider tip would have more self steering, but that doesn't mean that the tip has to be wider then the tail in order to get any self-steering.
The tail is mostly aligned with the direction of travel, which is why its being deflected less then the tip, and thus causing the rotation.
Think about this. If you are in your car and you put your hand out the window and point your fingers forward and hold you hand so its pointing exactly in the direction of the wind. now bend your fingers a little bit while holding your palm heel more or less still in line with the direction of the wind. The wind will push on your knuckles and cause your hand to rotate towards the direction of your fingertips. Different curvatures of your fingers will have more or less effect on rotating your hand.
This is more or less what happens with your shovels in terms of self-steering.
Back to my unanswered questions:
Does this self-steering effect cause the tails to fan out?
Will this self steering effect be increased or decreased by increasing the edge angle?