If you have access to a serger, one that sews the seam and serges at the same time, this would be the time to use it. Otherwise I would overcast or zigzag so that it doesn't unravel. My daughter-in-law made a satin quilt for her friend as a wedding gift. It turned out quite beautiful but she had trouble with the edges fraying. She didn't have any problems with the fabric waving,though.
Good luck!