I just changed the battery in my Kindle DX Graphite (9.7" screen, serial starts with B009...).
My experience with my particular model involved no case breaking at all (not same model but thought I'd share what's typically involved).
I bought battery off ebay ($10-$15 range) and followed youtube teardown video (pop off top plastic back piece, unscrew two screws, back case slides off. old battery popped out, new battery inserted, reassemble).
In my case I'm obsessed with the large screen of the DX so was willing to invest a bit of money/time to give it new life again.
If you're currently using the normal screen size, the Oasis is a sweet buy for sure (my wife has one and loves it).