If nothing else for the drawstring you could use those little beaded metal chains (like the kind that come with con badges), or you could hit a craft shop and see if they have any small chains for sale.
As for the necklace part, if you can't find any at a store, try ordering a handful of small chainmail links. I've done work with chainmail before, and since it's usually just metal wiring (though thick wiring), with a pair of pliers it's not hard to make a simple chain at all. You could probably order 100 rings or so from any number of fantasy-oriented armorers for a few dollars. (it'd be even cheaper to buy wire and coil it, but probably easier for a one-time deal to just buy some rings) You might need needlenose pliers for the size of rings that you'd need, though.
As for the beads, I heard somewhere that you can fashion them out of Sculpey.