I couldn't however find any commercial solution available, so I started building one using only things I had at home. The result is a super light weight, incredibly inexpensive shock mount for the Zoom H1. I didn't think of taking pictures while I built the holder and therefor I can only show the result.
The holder is basically a soda can which is cut up. I cut away a big piece of the middle section and then glued the end pieces together. Then I took a long rubber band and taped it to the can.
To fix the holder to the camera I used a hot shoe to tripod screw adapter, which I glued to the holder.
Good luck and enjoy!