@essin, This, of course is a nine year old post, so forgive them if they're not up to date.
Battery replacement on many Nano models requires soldering, including this one. iFixit seems to avoid repair guides for devices that require soldering, as it is apparently considered a more advanced skillset than the average person possesses. I don't disagree entirely, but there are a host of repair guides like this one that aren't being made because of that restriction.
None of the repair sites like this that I'm aware of have guides for Nano batteries, probably for the same reason. There are, however a host of YouTube videos out there that do a pretty good job of stepping you through the repair. Here's one that looked pretty reasonable to me.
[link|https://www.youtube.com/watch?v=U_N55_Tdz2U|iPod Nano 7 Gen. Battery replacement - YouTube|new_window=true]
The batteries themselves are readily available; a quick internet search turned up dozens on sites like Amazon, eBay and AliExpress among others.