I love this thread, as travel photography and gear choice is something very close to my heart. I've had the good fortune of traveling around Australia for work in the last four years, as well as taking trips to China, Hong Kong and Japan. Each time I've taken a number of cameras based on what I had and what my interests were.
For the OP: if you have a M6, heck, take the darn M6. As everyone says, it is meant to be used and can be replaced if necessary. But definitely take a secondary camera. My preference would be for something that shoots in ways or situations that the M6 cannot, which would mean things like:
- wide angle digital compact like the Ricoh GRD III, Canon S95, Pana LX3/LX5, Olympus XZ-1 or Samsung EX1
With a camera like this, you can shoot with wide apertures and keep the ISO fairly low. You'll get a very quiet and versatile camera that can go in a pocket, depending on the camera you choose, and in the case of the Canon and Pana, take decent video.
- high quality travel zoom like the Sony HX9V, Panasonic TZ22
If wide apertures are not as important, but zoom is, then a good travel zoom is an excellent choice. I am consistently impressed with the photos and video taken by the Sony. And for a trip around the world, I think that video is wonderful.
- tough compact like the Panasonic TS3
Something you can stick in a pocket and even taken snorkeling if you have to. The recent Panasonic waterproof compacts even have decent image quality, and the shutter sound is so quiet you won't even know you took the photo.
A compact digital as your secondary camera will give you a lot of flexibility, as you can take snapshots of anything and everything that takes your fancy, get decent video if the camera supports it, and if it has zoom it greatly expands your shooting options compared with a prime on the M6.
If I was going on a world trip, I would take a Leica body and two or three lenses, a large sensor compact like the Ricoh GXR and 28mm module, Sigma DP1/2 or Leica X1, and a compact like the Canon S95 or Ricoh GRD III. There have been times when I've only taken a GXR and two modules on a short trip and been very happy, but I know that on a round the world trip I'd desperately hanker for a Leica body and decent video.