You might be able to use something like this....
Chamfer Plane Link
Generally used for woodworking, but styrene is pretty soft stuff...probably wouldn't be a problem with this tool.
It'd take some adapting, but depending on how much of this you have to do, it could be a time saver as well as provide consistency.
Not sure what your project is, but in general I would be doing what Lee suggests....with a homemade fixture. I'd take a scrap piece of hardwood...say, oak or maple...and cut a 45-degree bevel along an edge. Then I'd clamp the styrene edge just 'proud' of the bevel. Running a regular ol' file along the hardwood bevel will shave the styrene preferentially over the hardwood. In fact, I have several rather dull files (seen better days doing yeoman's duty on metals) just for smoothing softer materials....like styrene. Those old and dull flat b_stards (just like me!) couldn't cut oak or maple if my life depended on it. But they love their second life on wimpy stuff!!
So, as always, FWIW.....
KD
BTW....re using power tools....saws, routers, sanders, etc....too much speed will 'melt' the edge rather than cut it cleanly. We're talking 1/16" styrene edges here....I think God gave us enough 'power' to cut a bevel on this edge!!!