Fun! I like the idea of this assignment. Well, one possibility would be to think about which wishes would turn this story from a horrific tragedy with overtones of terror and despair to a farce which helps us to learn a similar lesson but through focusing on satirising humans as always wanting what we can't have but then being unhappy when we get it.
You might like to think of an issue that is important to us in this day and age, such as plastic surgery and looking young and beautiful. In my version of this story, a playful Mr. White picks up the paw and asks to be young and handsome again. However, this wish has become so true that he is more successful than his son and becomes something of a playboy, much to the chagrin of his wife, who becomes very upset. Finally, after much browbeating, he agrees to his wife's entreaties to become young and beautiful and this is his second wish. However, it is now his turn to be annoyed as she becomes the lover of various Hollywood actors and politicians. So annoyed with the paw and with what it has done to them both, he makes his third wish, wanting the effects of the first two wishes to be negated.