I would back the full cut out with a fusible and then trim it to shape, and fuse it to the sweatshirt. Read the directions for your fusible though, as some fusible might not be strong enough to penetrate that heavy of fabric. You may need to use some pins as well before attaching it to your sweatshirt. I would also place a tear away stabilizer under the sweatshirt you are fusing to, and stitch a straight stitch outline in matching thread on the piece being appliquéd , to hold it in place, then go back and do the zigzag...... just my thoughts. Years back I did a similar idea with an eagle shape, but it was cotton and fused it to the front of a sweatshirt.