Sounds like you already have the words printed on the fabric. If it were ME, I would do fusible applique. I don't know about satin stitch, so I can't help you there. But I do applique and have appliqued letters on wall hangings many times. It turns out so nice. Then you can stitch around the letters. You can make the letters exactly the same as the ones you printed on your fabric and lay them over the printed words. Just my advice. But that's because it sounds like satin stitching can cause problems if not done correctly.