You guys seem to have this pretty well covered but just thought I'd include my experience as well. A few days ago I replaced the damaged housing on my International One S because somebody was interested in buying it but then wasn't interested in my asking price because the warranty was now void..
Anyway, it was super easy. Only difference is that, while the one in the video's lower cover just pops off, mine is double-sided stickied in an elaborate pattern and was rather difficult to remove. The sticky stretches out and needs to be put back into place. It was even more difficult to get it back on properly.. but I finally got it.
But yes, The battery is easy to get at, but I don't remember seeing a connector for it (but I wasn't really looking for it specifically.. just checking things out). So I wonder if the EU version is soldered and the US version is connector?
I refuse to have a signature.