I would cut the freezer paper pieces out by hand.
What I do is use a Sharpie permanent marker to draw the shape on a piece of freezer paper. Then I stack about 6 pieces of freezer paper on top of each other, with the traced shape (not cut out yet!) on top. I iron around the outside edges; this "glues" the sheets of freezer paper together. Then I use paper scissors to cut around my drawn shape. This way I get 6 pieces for every tracing and cutting.