I would starch the fabric heavily before cutting.
What I do is mix Sta-Flo liquid starch 1:1 with water, "paint" this on the fabric with a wall painting brush (my kitchen island is the right height), throw the starch-saturated fabric in the dryer, and then iron it with steam. The fabric ends up being similar in stiffness to lightweight card stock, and any bias-cut edges don't stretch.
I would not use even a lightweight fusible because it makes the fabric permanently stiffer. The starch will wash out completely and leave the fabric with its original softness and drape.
Incidentally, starching also helps prevent any stretching when machine quilting. I use the same starching technique on my quilt backing fabrics before layering, as then I am sure there will be no tucks or puckers. I also use this technique before cutting bias binding strips.