OK some proper step sanding will work great much better than file.
Sanding cues or wood for that much is all about useing good paper.
Gator grit,3M or any 3M brand or style that is wet\dry sand paper med. grit.start with 220,320,400,600,800,1200,1500,2000 this is for the whole cue you should have the marks out by 400 or 600 otherwise go back to 320 or . I assume you know how to keep paper clean from clogging this is very important but if you use poor qaulity paper you will get piss poor results .It should be very easy to sand out the router marks also when you taper the next cue rest you r hand on the cue as the router goes over the rings you should be turning the cue slow on lathe and useing at least a laminate trimmer router of some kind (high RPM)