Just watched a how-to video (https://www.youtube.com/watch?v=oEmlPK9R6Og), you better be the electronics DIY guy for that.
I followed an ifixit.com guide (like this: http://www.ifixit.com/Guide/Replacing+iPhone+3GS+Battery/154...) which, combined with the video, was very easy to follow.
Alternatively, you could probably find somewhere to do it for you for maybe $50 or so (still cheaper than Apple), but I doubt they'd use anything more than the cheap stuff you find on Amazon.
Still, it's worth following the other suggestions first and seeing if you can downgrade the iOS version.