I did this using just my hands and a pot of boiling water and it took all of ten minutes. I learned the trick from mye28.
First, be absolutely sure to mark the relative positions of the two cages (rotation) and their depth on the old motor shaft. You can use a sharpie to mark the old shaft and measure it after the cage is removed, then mark the new one. The cages are precision balanced using little metal clips and moving their position will upset the balance. Don't lose or move any of the little metal clips. Also be careful to handle the cages by their strongest point where the 'disk' attached the outer fins to the center so that nothing breaks.
Boil the pot of water and put one of the cages down in it (hold the motor). Count to ten and pull and twist the cage off. The boiling water will have made the plastic softer and swell so it can be removed. Quickly put the cage on the new motor up to the marked point. Don't worry if you don't get it all the way, you can always put it back in the water to heat it up again.
Repeat for the second side and align the marks on the cages so they're in the same position relative to each other. And you're done. The whole thing took me less than an hour with the longest part being the removal of the heat shield in the engine because the bolts kept rounding off.