Thanks everyone for the suggestions.
I don't think I'll be going the desiccator route. As I said in my first post I don't want to start importing equipment, even if I can.
I'm not sure that wax paper is available here but I'll send my intrepid team of sleuths out searching.
In the meantime, I'll try the freezer / partial defrosting thing which a few people have mentioned. I'm not going to put frozen cheese on my pasta, so that is a non-starter. Washing the cheese in vinegar doesn't appeal either.
By the way the box grater is not what I "prefer". It's what I have. Out here, you have to make do with what you can find, which in many areas of life isn't a lot.