I'm planning to customize some CPU cases for optimization in a internet cafe setting. The setup usually is that CPU's are placed under the tables and in a row with one side facing the open (where the chair is).
What you're looking for is called a tower or enclosure.
Modifying an enclosure for airflow in that way will disrupt the airflow over the components inside. The power supply exhaust will be difficult to move as you will need to mount the power supply in a completely different position. I'm not saying that what you're trying to do is impossible but I certainly can't recommend it.
A better solution may be to look at today's small form factor computers or even all-in-ones. In a cafe environment where the machines must be grouped closely together, smaller machines wouldn't need to be very concerned with airflow.