Would it not be possible to request for your exam invigilators to provide you with a piece of paper at the beginning of your exam and leave it on your assigned desk as opposed to this?
I know in the past, back when I was doing my A Levels, they said you can request additional sheets of paper if needed, so I don't see why you can't ask for it before the exam begins and simply ask them not to collect your paper as it was for scrap notes?