I've never sewn an icord onto something, but I have knitted them on.
What might work really well is to pick up stitches through both of the pillow edges. Then you can either purl back or cut the yarn and start the icord at the other edge so you can do it on the knit side that you picked up. Then you knit 3 and slide them back onto the left tip. Then *k2, k2tog and slip those back, and keep doing that until you run out of stitches. If you wanted, you could do it all around the pillow edge in one shot. Just pick up extra stitches around the corners.