Hmmm, I have not made fairy wings from foam core, but I did from lightweight stretch fabric and wire, with a jersey that had an extra pair of arms sown on and connected to the real arms with fishing line.
Another possibility is to get some mylar gift wrap from the dollar store, wire, and a hot glue gun that can also come from the dollar store. A cheat is to make the top and bottom wings with different colored Mylar wrap.
Tissue paper wrap can also be used, and either can be decorated with glitter glue.
Again, the dollar store may be your friend.If you don't like the wire, or think that it is too complicated then you can make the foam core wings that you described, and glue the mylar over it.
A quick Google found this -
A paper lantern and a glow stick can be used to make a firefly instead.
The Auld Grump