Well, here's the result of my experiments over the weekend. The insulated cup is on the left, and the two cans used to make it are to the right.
The cap and a small part of the sloping sholder of the inner can had to be cut off to allow it to mate with the remants of the cap of the outer can. The two parts are held together with Araldite (cleaned up after it set, to remove as much as possible from contact with the contents).
The space between the cans was then filled with expanding foam, and the base put back using the usual drinks can burner assembly techniques.
I need to refine the foam-filling method, as the foam expanded in a bit too much, rather than up, so the inner can has buckled into a nice pentagonal shape...
I haven't done any timed tests, but when I filled it with boilding water, the outer remained cool for a good while, with heat coming up from the metal:metal contact at the top, and then down the rest of the cup.
I made a cap by taking the ring pull off a full can, and then removing the cap before opening the can. This sits nicely in the opened cup.
The completed cup weighs 24g.