I have appliqué quilts my grandmother made in the 60's and they have the button hold stitch in black. Her fabric prints also became meshed together because of the colors but the black made them pop. Good luck this is a tough decision.

Roc Rak would not work with all the angels and truns. I would use a dark background, black or navy...,navy was very popular in that time period. Then I would use a close blanket or appliqué stitch. You could also fuse some lightweight stabilizer on the back of the fan blades and trim around the edges evenly. This will all but eliminate the fraying. Be sure to post when you complete it, would love to see it.

I like the buttonhole (or specialty stitch) idea too, but I'm also wondering weather a stabilizer or even some lightweight interfacing might help keep everything together.

Do you have your heart set on this background? I would like to how it would look with a medium or dark brown.

I picked up some Dresden Plates at the thrift store that were hand pieced. Just the Dresden blades so I need to put them on fabric squares. Because the hand piecing is a little loose, I am going to use the method Terri D posted & then use a blanket stitch. That way the plate seams will also be stabilized.

I would use black rick rack ay at all....or maybe change your back ground material to an off white with a TINY red flower print.

No, to the rick-rack, it would be a mess to do, #1, and it would not look right. I would do the button-hole stitch and if you want contrast, use a variegated thread or some bright color that complements the fabrics. JMHO

I would line them by laying them on a piece of white fabric and sewing a standard 1/4 inch seam all around the outside edges, then trim the white to match the block edges and turn through the center. You will need to clip the deep v before turning. Then add a dark center and decide if you want to do a blanket stitch in dark thread or not. They are very pretty with lots of variety and worth saving.

The stabilizer is a great idea. You don't say how many squares you have. Why are you finishing the edges instead of joining the squares? If you only have a few, how about stabilizing them, then have them each framed? I see them with the edges unfinished, but placed on a matting to accent the colors in the square.

I would do what TerriD suggested, with the fusible facing. In the long run you want a finished edge. And rick rack points curl after washing, and require pressing out individually after each washing. I'm old enough to remember that tedious job.