I would say to cut around the flowers and put them on new backing but some of the flowers look like the petal tips go right to the edge? I think I would place the flower (block and all)on top of the new background fabric and straight stitch around the outside flower petal edges inside the original hand sewing. I would then carefully trim away the white background and see how they look. You would perseve the original sewing, the flower would have the white behind to add stability to the fabrics and the flower petal edges would kind of fray up like raw edge appliqué?