When you get the cluster out, take a good look at the square socket that the cable fits into. There's a Robertson screw size that will fit right in. Chuck that into your drill, put the drill in reverse, and insert. At maximum speed, you should see about 40mph (or whatever, I forget now). If the speedometer registers, that's not your problem.
...and no offence to the mechanic, but if you look at the depth of the socket in the speedometer head, there is no way a steel cable is going to shrink that much to withdraw it completely out. The casing collar might have loosened though, enough to allow this, but it's got to be very rare IMO.