When Harry and Draco met in PS/SS, Draco detto Narcissa was buying him a wand and Lucius was getting his books. If the wand chooses the wizard, how could Narcissa get him a proper wand?
It is possible, since Draco's dad is a wizard and his mom is a witch, that he has had a wand before Hogwarts. Therefore, all Narcissa had to do was ask the wand-maker (sorry, don't remember his name)for the same kind of wand. Just like when Ron's wand broke and he got a new one without having to hold every one all over again and see which one worked for him.
