You might try straight stitching by machine around the edges. That's a perfectly acceptable way to applique. Sounds like some pieces are too narrow to do a blanket stitch on both sides. Another suggestion is to sandwich your piece and do close all over stitching and not worry about stitching each piece. Since it's a wallhanging you probably won't be laundering it so your fused pieces should stay put. I have a similar applique wall hanging with long narrow pieces, and the pattern suggested the all over quilting method. I haven't done that because I have never done any machine quilting except straight lines with a walking foot. Perhaps someday I'll learn how to FMQ and be able to finish my hanging.
Jane