Inside, there was some odd, rubbery, fibrous insulation tape on the top wire. I assumed this wasn't the best in the world and cut it away. The old wire could then be unsoldered and replaced with some new silicon cable complete with croc-clip.
The wobbly leg was fixed with lots of superglue run around the inside. Not ideal, but I couldn't take it apart to do anything else. The fix worked, so that's all that matters.
With the back back on, and a quick clean of the glass on the front, the job was finished. OK, I still don't really need another voltmeter, but this one is pretty good looking so I'm glad to add it to the collection.
