1. Removed the batteries, then removed the five screws showing in this photo above, as well as one on the other side.
2. The speaker wire was not difficult to find after opening the remote. It's the yellow wire (note arrow) that connects the speaker to the solder points marked "SP" on the circuit board.
3. The picture above shows the bottom view of the solder points for the speaker. I gently heated these points with the soldering iron -- keeping slight tension on the wires as I did so -- until the wires pulled out.
4. I reassembled the remote, which is now completely silent. Now Maisie can hang out with her smelly wino friends at Fisher Price's GeoTrax Grand Central Station without being scared away by the noises.