Maybe simply top stitch it onto the background fabric possibly using pins to hold the fur out of the line of stitching and once the pins are removed, the fur would fluff up to cover the machine sttiching. The concept sounds very interesting and I don't think it would be that difficult. You could use a glue stick, even just to hold the piece in place long enough for you to use a stright stitch on your machine to secure it permanently. I'd love to see photos as you go along if possible.