Hardware Wii U GamePad display descratchify

[LeNoobio]

Hello!
Before I try anything stupid I rather ask around if anyone has some experience in removing scratches from the GamePad's display/touchscreen?
I have a rather deep one (I can feel it when moving over it with my stylus) and I was thinking of carefully removing it with very fine sandpaper and then polishing the display afterwards.
How stupid is this idea of "fixing" it? (I kinda fear it'll only get far worse by attempting this )

Note that I already have a replacement screen I could use in case things go terribly down the shitters.

Thanks for any thoughts

 

[PewnyPL]

Someone else would have to confirm it, but the very top of the 'screen' is either just a transparent plastic OR it's the gamepad's touch panel. In the first case using fine sandpaper would work. In the second case you should not do it, as it will likely screw out the touch control of the screen.