A turn table that rotates the item to be scanned in 15 or 30 degree increments.
With a stepper motor you have good control over the amount you've turned the table. You could also use geared motors but then you'd need some sort of feedback to know the table's angle.
An arm holding the laser that enables the laser line to 'very slowly' and smoothly pan up and down over the item to be scanned.
Does this have to move linearly up and down, or can it be fixed in the center of the obect and rotated. If the second you could strap the laser to an RC servo. If the first then probably some threaded rod and another stepper.
An Arduino is not an overkill, this is a good sized project for one.
Rob