As I moulded the hands around the wire, it was easier and far sturdier than trying to attach the wire all separately to the hand and the record. 

 

However, there was still the issue of sturdily attaching the hands to the record itself. I first tried large balls of blue tac; this failed as the speed of the record player sent them flying. I then had the idea to bake some small supports out of polymer clay. These were simply cylinders that had a hole in them the exact size of the wire- that is what I love most about polymer clay; it doesn't change shape at all when it is baked and hardened!

Fully assembled zoetrope: