A straight stitch will definitely fray more than a zig-zag/satin stitch. One option that helps a bit with that that I've seen (and it also look really nice) is using a twin or triple needle. Or, if you're going to be custom quilting this, you could just do individual parallel rows of quilting & have it be a one-step quilting-applique (i.e., just fuse the piece down & leave it be until it's time to quilt it).
Another option you can give your client is Fray Block. Yes, it dries just a little stiff, but it's not bad & it helps a LOT with fraying. If you have any pieces -- especially small or narrow pieces -- that are cut on SOG, I would strongly consider this for any true raw edge applique (straight stitch only) or you will end up with a furry edge after just a couple times through the wash. Of course, some people love the furry edges so maybe that isn't even an issue, but if she isn't one of those people, Fray Block is a great tool to have on hand (Fray Check dries much stiffer than Fray Block). With enough exposure to the sun, it can change from clear to yellowish, but that's the only issue. It washes well & is virtually invisible.