I just had someone on another forum message me asking if I could fix the damage they did when they tried to redo the brushed finish on the top of the lugs on their watch. They completely rounded off the sharp corners...they are getting a new case from the manufacturer as a result.
In my experience, trying to refinish a case that has just normal wear on it, is far easier than refinishing a case where the owner has done some home refinishing, as that almost always makes things worse. You will most likely not get the finish to look original, and risk doing damage to the case in the process.
My advice would be to leave it until the watch needs a service, and send it in for a service and refinish then.
Cheers, Al
