I was actually not replacing a battery at all. My buddy's headphone jack was really worn down and was doing the mono thing unless you pushed on the wire. I got a Hong Kong special rear shell with headphone jack and hold switch included, so the battery stayed.
Repair went pretty smooth. Not the first Classic I have opened but this was certainly the easiest time I've had doing it, by far. Pretty sure I owe that all to the use of the putty knife.
The putty knife was key. I got a 2" knife from Harbor Freight for a couple bucks and, although maybe unnecessary, sharpened the end a bit so it would slide in better. This made getting leverage, minimizing damage to the rear case and popping the clips SO much easier than without it.
I also have a Harbor Freight 6-piece crafting/carving set which basically looks like a bunch of dental tools. Each one has a different tip on either side, from scoops, to chisels, to hooks, so they help out a lot. Just need to be careful using anything metal around sensitive stuff that can get damaged easily.
And I ALWAYS make sure to test the thing before snapping it all back together. You do not want to accidentally forget to hook a connector back up and have to open the thing again. Get everything connected, gently rest the top on the bottom, take it off hold, and see if all is well before you move on to those oh-so-satisfying snaps of popping the case back together.