Tom, Shozam will need to re-compress images whenever it process them. So if your images need to be scaled, you cannot get around the fact that the program will need to re-compress as well. Compression is part of the unavoidable process of saving a JPEG image and the image will need to be saved again after it is scaled. Setting image quality at 100% will make your images very large without a noticeable improvement to image quality.
I recommend you keep your original images at high quality and use about 80% quality setting in Shozam. You can test the trade-off between image quality and file size by generating a few test runs, evaluating images visually and right-click on the image to see the actual file size.