A few years ago Kevin and I were in Kanagi for a tournament. One if the vendors was selling a device that muted the shamisen. It was actually a dou shaped piece of rubber I believe. It fit right over the skin and made it completely quiet.
Anyway, it was something like that.
I recently bought a similar mute/shinobigoma as I live in an apartment in a rural area that’s really quiet at night. I don’t have it handy, but if anyone is interested, I can upload a picture of both it and the box later.
Basically, it’s a long flat board-ish thing, that rests on the edges of the dou, so not putting pressure on the skin itself. It’s covered with thick washi (Japanese paper) and a bachikawa, and has an adjustable bridge affixed to it. (you turn a little screw to move it up or down.) To put it on the shamisen, you actually have slide the neo(or whatever that knot thingy is called) off as it has a little tail piece that hugs the curve of the dou and keeps the mute from moving while you play.
I was a little leery about it, but was assured by the shop keepers that the bachi would be fine. (Though mine is synthetic bekko, so I’m not sure about the actual stuff.)
I haven’t used it too much yet, but am happy with it so far and am pretty confident that it’s not harming the instrument at all.