Can I modify the plug of my new bath fan to fit the non-polarized receptacle?
No, no, no!  It's polarized for a reason.   

Just replace the receptacle with a polarized receptacle.  Make sure the taller slot is on the neutral side.

They look like this, note the absence of a ground pin.  There may be a green screw on the outlet nonetheless, that grounds the outlet.  It should be left disconnected unless ground is actually present in the box.  This is a current product legally sold all over in white, ivory or brown. 



As a footnote, this is a polarized receptacle.  The other type, with 3 slots, is a grounded receptacle. If you really need one of those, there's a legal way to do that using GFCI's.  As such there is never a reason to break off a ground pin.