All the previous answers are good advice. Just the same, I would be very nervous routing an edge (roundover?) near where screws were used. A big bit like a ¾" roundover bit is hard enough to control with a hand-held router under normal conditions. It would be much more effective and safer if you use a table mounted router. Hitting a steel screw with a router bit should be avoided, it could be very dangerous.
I'm not sure how much material a ¾" roundover bit takes off, it depends on how deep you go. Before doing anything I would test things out on a piece of scrap wood. Put in several woodscrews a variety of distances from the edge of the scrap wood. Start at 0.37" from the edge and work your way in further away from the edge. Pre-drill the holes including a counter-sunk hole for the screw head, drive in the screws, and take them out. Then route the edge and see which holes are far enough away from the router bit.
For a subwoofer, a rounded over edge on the front baffle may be nice looking, but it serves no acoustic purpose like it would on a normal speaker. If you must use screws, maybe you should skip the rounded edge.