I would probably fuse them individually on to a very light muslin (or similar) to stabilize them, then piece together. I recently did a string pieced mug rug using an old piece of sheeting as foundation, thin batting, then a remnant piece of cotton fabric for the back. I handquilted this with no problems at all, perhaps you could do a test block to see how you go.
Would love to see pics of your blocks.....you know we love pics
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