I'm by no means an expert, but this is what I think:
It would be a balance issue to allow a character to use a two-handed weapon in one hand because it is effectively giving the character the Critical Modifier bonus without the inherent penalty of having both hands busy.
What I recommend is to make him use a one-handed weapon and pretend it's a two-handed one. For example, he could use a Two-handed Sword that costs, weighs and does Medium Critical like a Long Sword.
Now that I think about it, an easier way to work it is to make him use a Critical Modifier of a lower size whenever he is using the weapon in one hand.