A rasp probably won't give you the smooth edge you're seeking, even a fine hand-stitched one (very expensive) or one of the superior machine-stitched rasps (usually much cheaper but not always) that work as well. Rasps are superb tools and capable of surprisingly accurate work but they're for faster removal, not for the finest finish.
If you want to do this using a similar tool one or more files would be a better choice. This is a gross oversimplification but a double-cut file will cut faster but leave a coarser surface and a single-cut file will leave a smoother surface.
If you don't currently own any files I can highly recommend them for working wood. For now though you can do without — simply glue some abrasive paper to strips of wood (paint stirring sticks are very popular for this if you have a source) and use them as you would use a file*.
In addition to being super-cheap these 'sandpaper files' have an advantage over real files in that they can be used on both the push and pull strokes (the teeth on files only cut properly on the push stroke) but note that working the edge of plywood you'll mostly want to confine yourself to push strokes only, stroking downwards or away from the surface. If you stroke backwards you risk lifting flakes of the face veneer which can be impossible to neaten up properly. You can stroke sideways as well, but the exact orientation of the grain in the veneer relative to the cut edge will dictate how well this works.
This is a common tip for working plywood and it applies here as well, it's very helpful to strongly knife your marked lines beforehand. If the knife cut is deep it can completely sever the fibres of the face veneer virtually eliminating tearout if you're careful.
*As an alternative to this you could use emery boards of course which are much the same thing, but you're limited to a fairly small size and to some extent the range of grits available.
