If it's empty then you can use a torch, go to tap plastic and they will teach you how to do it, last time I visited tap plastic on Florin the manager used a piece of scrap acrylic, scratch it and then clean it up with a torch.
If you pratice enough time with scrap pieces, should be pretty ease on the real thing.
I have been removing many scratches on plastic lens (auto) for a couple of years now using NOVUS and a good buffer like a Porter Cable, doing it by hand would works just need a lot of time.
Those method are for dry products, if you have water then Marc have a better way of removing those scratches.