That's a 4th gen iPod then, presumably with the monochrome display, sometimes with a color one. It is not the Classic, it's 2 generations before that. I would not replace the battery on it, instead I'd replace it -if you want to keep using an iPod- with a 6th gen iPod Classic.
The reason being that your iPod is an older model that has neither the good screen of the later ones, nor the best sound quality. Even if none of that bothered you, you cannot switch the HDD for a SD card. So battery life will never be great, it will always be rather heavy, and HDDs don't live forever. (SD cards don't either, but they aren't heavily used in iPods and should last much longer.)
The iPod is now so old and almost a relic at this point, this will likely be the last iPod you'll ever have. To me this would be a question of "what iPod do I want to use for the rest of my life" and I'd want that to be one of the latest models and not an older one.
If none of that bothers you, there is a guide on ifixit and it's not too hard to replace the battery, you can probably still find one on ebay. But this iPod model is pretty mediocre, the only stand-out feature it has from other players is the clickwheel of course.
I'd get the iPod Classic, officially that's the 6th gen. However, I recommend a specific version of the 6th gen that is inofficially called the 7th gen. It can easily be recognized for the black model, by having exactly 160GB, and on the black model the housing/front is not black, but a dark grey, and the clickwheel is much darker (actually black).
So the housing is dark but not black, and the clickwheel is black and darker than the housing. If you see that, and it's got 160GB, that is the very latest/last and best version of the iPod ever released. (On older black models the front housing is actually simply black, and the clickwheel is brighter than the housing. So with older models the colors are reversed.)
I have one such 7th gen with an SD card from this place:
https://www.iflash.xyz/
When you open the back to replace the battery (and install that SD card if you want to) you have to bend the back plate open, and you might damage the back plate in the process. This is fine, because you can get a brand new replacement backplate cheap on Ebay.
The only big issue with the iPod Classic and opening it up is something else that cannot be replaced and has to be handled extremely carefully: The port on the mainboard where the battery is plugged in, it is very loosely attached to the mainboard, and you need to remove the battery plug very gently, otherwise you'll rip the entire socket (port) out and then there is no way to re-connect the battery without soldering.
And because of that, I recommend that you disconnect the battery as few times as possible, only once if you can. That means installing the SD card kit and replacing the battery all in one go.
Overall it's simple enough.