Accepted answer: no
In the Joystiq review of The Cave, there is mention of alternate solutions to the puzzles (emphasis mine):
There is truly unique pleasure in seeing the dark, reprehensible turns each puzzle takes, and knowing that an alternate solution exists in there somewhere. Ron Gilbert assures me there are unselfish ways toward success, though I prefer the evil ones.
However, I can't find that there actually are unselfish solutions to the puzzles. The only thing I have found is this:
At the very end of the game, you can give the item back to the guy at the gift shop to get the alternate ending for that character.
But that is only at the very end of the game, after you have solved all the puzzles the same selfish way.
So, are there really alternate solutions to the puzzles?
Taking the Knight for example:
If you return the item at the gift shop at the end of the game, you get the "good ending" where the princess is saved. But as far as I can tell, the only way to solve the knight's puzzle is to release the dragon to kill the princess. Is there a way to do the knight's puzzle that will not cause the dragon to kill the princess?