Jan,
There are several factors that go into deciding how to treat raw edged fusible appliques. Is the quilt going to be washed? It sounds like it is going to hang on the wall. Do you like the look of raw edges? I personally don't, even though I know that Laura does not finish her edges. What kind of fusible webbing did you use? Some of them hold better than others. How much quilting are you planning on doing? Sometimes the quilting is sufficient to hold everything down if it isn't going to be washed (like Laura's)
If it were me though, I would probably stitch the edges with a very narrow blanket stitch using monofillament thread or matching light weight thread such as Bottom Line or 100 wt silk. I would put my open toed embroidery foot on the machine and set the stitch all the way to the right. Narrow the stitch and shorten the stitch length. then (slowly) stitch it down running the right edge of the foot just along the edge so the outside stitch is on the quilt and the left zig over is on the applique. Make a practice piece and practice first to get the tension and stitch width and length right first and give you a practice run.
Sometimes it looks fabulous to stitch it with a contrasting thread., but I think it sounds like you might want the stitch not to show very much. Also, it sometimes looks nice to use a satin stitch zig zag thread. Depends on what you like.
Look forward to seeing the finished result.