I do a lot of fusible applique. I like steam a seam 2. For the first time I was in a swap, I did not have the batting behind the fused pieces. A blanket stitch worked just fine, didn't need stabilizer.
I don't use a satin stitch as my pieces tend to be small. What I do instead is just FMQ around the item I've fused on. IF you do this 3 or 4 or 5 times around it looks like you've satin stitched. You can catch all the edges. Since almost all of your stitches were on the fusible you do not need to add a stabilizer. I like the way it turns out. I start and stop as you would for FMQ.