I wouldn't dink around with the freezer paper ...
Fusible web (double fusible webbing) is not hard to applique through, but all you are going to do is a blanket stitch, or it can't be done with invisible stitches.
Another fusible is only fusible on one side. You can create a fusible applique, do the invisible stitch if it is preferred. You copy the pattern on to the fusible, put your fabric right side facing the glue side of the fusible (forget the iron for a minute <g>)
Stitch RIGHT ON THE LINE ... cut 1/8 inch or more seam allowance and then cut a slit in the back so you can turn everything right side out.
Right side out is: The right side of the fabric facing out and the GLUE side of the fusible facing out ... now, what you have is a fusible figure that you iron in place on your block and the choice of either doing a blanket stitch all around OR invisible stitching as your choose.