Wood – How to remove sheet metal screws from the wrong side of a wooden board with minimal damage

I just took over my first apartment, and have to replace the kitchen fan. In order to fit my new kitchen in the cupboard above the stove, I have to remove 6 sheet metal screws pointing out from the sides on the inside of the cupboard.
The cupboard is made of some porous kind of cheap wood.

The screws have been screwed in prior to the cupboard (and kitchen) being assembled, so the "hat" of the screws are stuck in between two cupboard walls, and I am completely unable to reach them without dissassembling the cupboards from the walls.

Here is a hideous illustration of approximately what it looks like:

The 6 tiny lines signify the screws pointing out on the inside of the cupboard, while the hats are shown by the red dots.

How can I get rid of these screws while causing minimal damage to the cupboard?

Thanks in advance.

Edit
The screws were there to keep up a wooden shelf inside the cabinet.
I need to fit a new kichen fan inside the cabinet, so I tore off the wooden plate, but got no clue how to remove the remaining metal screws. They don't support the general cabinet structure in any way.