I wasn't sure how exactly to do it. I have little professional metalworking tools. But I did have some sandpaper S/C 120. I decided to sand away the offending logos. But first I needed to protect the crystal, which was accomplished by placing a large sheet of that sticky roller paper for removing lint from your clothes over the crystal, pressing down firmly and then cutting it exactly where crystal meets bezel, with Xacto type knife. Ready to go.
I found that the sandpaper would be very slow going. Though the letters were not engraved very deep, the sandpaper didn't remove metal as fast as I'd like. Also, the sticky masking disk was getting very tired and threatening to come up in some places. I tried emery boards for better purchase, but still about the same level of obliteration, very slow. I decided to go to the hardware store and get one of those triangular metal files, I think it was XX or X grade of cutting. This worked fine, and I was able to remove all of the logos (I left little bits and pieces here and there as slight insults to the original logos.) Below are the results. I think it's ok, especially the results of the buckle, but I think the case turned out pretty good as well, kind of rough though. Maybe I ruined it in some ways, but I don't regret my decision. I could not find an easy way to get to the dial. If I could have, I would have stricken out SWATCH on the dial with a Sharpie. But I could not, and SWATCH is there, taunting me every time I wear the watch, making a mockery of this whole exercise.