I would also be interested in creative suggestions as to how I might inexpensively render the speaker permanently mute without pulling the whole device apart.
Here you go, I've figured this out. Follow these steps.
1) Buy the cheapest pair of headphones that you can find.
2) Plug the headphones into the mini so that the mini won't use the internal speakers.
3) Super glue the headphones in place.
4) Cut the cord so that the headphones themselves can't be used.