There Will Be No Foolish Wand Waving

Petunia Evans always wanted to be just like Lily. The thought of learning magic would make her giddy with excitement. However a rejection letter from the headmaster of Hogwarts blew that dream out the window. What would've happened instead if the wife of the owner of Flourish and Blott's had taken a bit of pity and shown Petunia that you didn't need a wand to do magic?