Remember, the nylon shell will not stretch, so the fit will be critical. Cut the pieces as large as you can, then use safety pins to secure the parts as you slowly work toward a good fit... lots of little safety pins.
You are right that you can stitch before cutting. Down will escape, but not too much if you: Stitch two parallel lines maybe 1/4 inch apart and cut between them. Try to shake as much down as possible away from the lines.
After you get a good fit with pins, double check by stitching it up with a zigzag basting stitch along your proposed seam lines BEFORE TRIMMING THE EXCESS. That will tell you if you really have the fit right. A loose zigzag with the top thread loosened a bit and contrasting thread color will be easy to remove to make adjustments or to pin and stitch the final seams. Once you get a good fit, chalk where you want the final seams to go, do the double line thing again to remove excess and stitch it all up.