It depends if you're okay with fraying (some people prefer the frayed edge look). If you do it in a 50/60wt cotton in a matching color or a 100wt silk in a coordinating color, the thread will not show up much as a blanket stitch (I do my stitches a scant 1/8") and then you can wash it on a regular basis & it can be touched without worrying about fraying.
I know a quilter who does all her fused applique with a blind hem stitch (and have seen online tutorials on that) but it just always seems to start fraying by the end of the first year. All those little pockets where the straight stitching runs along end up peeling and fraying.