Welcome to the forum, Bluesky.
If you are talking about the notches created by cliping on inside curves, I haven't had any problem with fraying when I stitch the appliques with either the narrow zig-zag, or vari-overlock, or blanket stitch.
If you are concerned, you might want to make a sample of one motif with lots of clips, using the stitch you are most comfortable with, and run it through a couple of laundry cycles with your regular wash and examine it for fraying.