"any old 24 hour wall clock" -- the finding of which is left as an exercise for the reader.
This is almost enough. You would paste the center part (the "world") on the hour hand but without the "time" and "time of day" rings. You would cut a smaller circle. Just remove the second hand altogether. Behind it, paste the full image, with noon at the top and midnight at the bottom. Now the world rotates inside the ring of time.
Now -- this is somewhat reduced in resolution. You could make your own image, using a rectangular world map and an image editor with a rectangular-to-polar function. Note that the South Pole has to be in the middle. If you put the North Pole in the middle, you would need a backwards 24 hour clock movement, and those are impossible to find.