You can work the sweater as written on circular needles and just knit back and forth--no need to steek and no need to switch up the stitches. It probably would be easiest to work it as written on circulars since it's not worked like a traditional sweater--you start with the back, go up over the shoulders, and down the front.
To get stitches onto scrap yarn, use a large-eyed sewing needle, or, preferably, a tapestry needle and just thread the yarn through.
I've even used a folded paper clip for this when I was at work.
