We know that a wand can choose a wizard.

But is there any canon information to indicate whether every wizard walking through the door of Ollivander's shop will be chosen by their "other half" perfect match wand?

Or is this "choosing" business more of a "pick the wand among those available that most closely matches you", in other words a local maximum?

Think of it as a difference between Sabrina the Teenage Witch "One and only perfect soulmate" and real human dating/marriage, where you only get to pick and be picked by the best matching person among those you know.