Does it say what kind if fusible? If it is regular Heat and Bond, that will not sew well.
If possible I back it with black and quilt it and stitch the black silhouette all at once with black thread. I would just do a straight stitch about 1/8 inside the edges.
If you don't want to do that, I would use a black buttonhole stitch all around the silhouette edges and then outline quilt it on the background once sandwiched.