A readily available rigging material is Invisible Sewing Thread, also available at Hobby Lobby. An equivalent alternative - basically the same stuff - is fly-fishing leader material/monofilament (Orvis/Cabelas/BassPro).
Perhaps a more forgiving material is EZ Line, an elastic thread. It stretches, stays taut, and forgives an errant finger poke (Wow look at that! Boink!). I got mine from Bobe's Hobbys.
Both cement with superglue.
Going the wire route -- stainless steel suture wire (medical supply house material or SmallParts). Got a tube of 0.006" material. Measure with a set of dividers, cut with a sharp blade on a piece of tile or glass. Wire cutters won't easily cut such fine material, rather bend it - and it will notch your good scissors. Roll on a cutting mat using an emory board/sanding stick to straighten. Glue in place with some white glue.