If you are using freezer paper, you can stitch most of it down and then loosen the edge underneath that is stuck to the paper with a stiletto and slip out the freezer paper before stitching down the last little section. If the shapes are fairly simple, you could use a light inner-facing and stitch it around the edge on the right side of the appliqué shape. You cut a little slit in the inner-facing and turn the appliqué right side out. This only works on simple shapes because deep V's don't turn well.
You can also use needle turn appliqué that is done without any paper behind it.