Check around your town before you ship it off....
There was not an "authorized" dealer in my home town either, but I checked with my local running store, who referred me to a jeweler in town who regularly changes them. While you are technically "outside the terms of the warranty" by doing this, most running specialty stores know of a reputable jeweler who can do this. It's really just a watch battery.
I've had my Polar HRM for over three years now, and he's changed the battery 4 - 5 times with no problems.
Good luck!