I use coated green floral wire. Coated part doesn't rust, won't harm your critters, comes in large packages at craft stores. You can use silicone on the ends so they don't rust.
I prefer the kind that's thicker and comes in lengths but you can buy a thinner variety of floral wire that comes in rolls.
You could probably just mold/wrap the wire around the driftwood in a manner that wouldn't damage the wood itself. Then attach the wire to that piece.