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If it's light it should polish out even by hand. I would avoid using any real harsh compounds and T-cut and get your self a tube of Meguiars Scatch X, formulated to work well by hand.
That's not a bad product, go easy on it as it can be quite abbrassive. You will need to follow it up with a lighter polish possibly as well, as it tends to put in very fine scratches while taking out the bigger ones!