Why not just use a satin stitch to attach the appliques? That way if you use flannel, you won't have to worry about the edges fraying. Although if you cut the piece larger than "Mario" and stitch inside the edges, the edges would fray and you would have a "rag" applique. I'm not sure how the cotton applique would look on the fleece.
Do you have access to an embroidery machine? You can do great "in the hoop" appliques with it.
Others may have more suggestions, too.