I use freezer paper to hand applique onto my background all the time. I usually hand baste the seam allowance all the way around the freezer paper shape and never iron it down. Then I hand applique the piece, stopping about an inch before the end. At that point, I remove the hand basting and finger press the seam allowance before removing the paper. It may sound like a lot of work, but it works for me and the basting goes quickly. I have found that this method allows me to avoid those little points because I can use my needle (I use straw needles to hand applique) to push small bits of seam allowance smoothly along the edge. This method also allows me to re-use my freezer paper shapes several times. Enjoy and use whatever method works for you!