Maintenance Re-stringing help

I restrung a pair of jointed hands not too long ago and used a beading needle to do it. Not the solid ones, but the ones made of twisted wire with a fairly large eye. When you start to string through the passage, the eye clamps down on the elastic. Having seen a picture of the doll now, another possibility would be a yarn needle.

 

Bending a piece of thin jewelry wire can also work to guide the elastic.
I've got few small dolls that require quite tight elastic and I do it like this to get enough tension:
I fold the wire in half around the elastic. I use the wire to feed the elastic trough the channel and then I roll the wire ends onto a dowel (or pencil, or the like) to give me a handle to pull on.

 

You can get some pretty small hemostat/clamps at places like Harbor Freight tools, they are restring godsends. I have restrung tiny dolls and hands without hemostats, but having a pair of them makes it so much easier. Also echoing having a piece of wire or a bendy needle can be a massive help. Also the using ribbon or cord to thread through the limbs and pull the elastic behind it trick use to restring bigger dolls can still work if thin enough cord/ribbon. Good luck.