Finding someone who can really professionally sharpen pinking shears is like finding a needle in a haystack( at least where I live)! Many places won't even attempt to sharpen them, or charge so much its cheaper to buy new. I would try cutting through some cotton cloth with some sewing machine oil on the cloth, to remove rust and season the metal. Also take the cloth( with a bit of the oil) and rub the shears going away from the blade bottom to remove any bits of rust. A tiny bit of sewing machine oil on the screw might help to free up the blades, but you might have to work it through by opening and closing the blades. Once the rust is removed and the blades move more freely you can evaluate if its worth the cost of sharpening.