Sadly, Apple doesn't offer any repair parts. So you'll need to find a junker to steal parts from.
Here's the IFIXIT teardown to help you on your exploratory surgery: [guide|1240|Magic Mouse Teardown]. If you jump to Step 11 you could checkout if the sider joints are OK on the battery contacts. Often the batteries leak and these get corroded.
If this is a bit much, I'm sure you can find a used one for about $30 ~ 50 US. A junker a lot less.