Use the ppm definition directly: 1 ppm is 1 part in a million by weight, so it equals 1 mg of SO2 per kg of product. The batch size is $100$ kg, so the total SO2 needed is $350 \times 100 = 35000$ mg. Converting to grams, $35000 / 1000 = 35$ g. Since KMS supplies this exact SO2 dose to the squash, the required weight of KMS works out to $35$ g. This rules out the much smaller values, 0.0175 g and 0.035 g, which come from a units slip of dividing by an extra 1000, and rules out 17.5 g, which is only half the needed dose. \[\boxed{35 \text{ g}}\]