if you choose to use fray check i would wait until it is all done then go over the areas you want-the fray check will put a line of (stiffness) where ever you add it.
i don't quite understand- raw edge applique always has...raw edges- hence the name- it is normal for the (hairy edges) that's raw-edge...
if you want to avoid that i would use a different applique technique- or it helps to use a tiny zigzag or blanket stitch.