I am trying to open the outer casing of the...

There is a push in type flat plastic switch trim cover over the metal housing surrounding the switch.. You must unplug the cord, gently pry around the trim cover and you will find a screw, an irregular one underneath holding the switch in place. DO NOT OVERTIGHTEN when reinstalling this one or you will crack the switch.

Once removed the rear housing will come off. Then you will see several new philips round head screws holding the front housing onto the vac.With all screws removed the housing should open easily but there may be dirty film inside holding the halves together. The fan shaft will unscrew revealing the fan, a spacer behind and perhaps two different spacer washers. Install the new fan hand tight, washers and spacers in same order...
Good effort figuring this one out. Please post back with results.