This was really helpful - I didn't have (and couldn't easily source) a spudger. I used a small flathead screwdriver instead. Probably not recommended as it could easily damage surrounding components, but seemed to work OK.
I wasn't able to remove the battery, largely because of the above (and the warning in the guide about pulling on the plastic tab), but was easily able to remove the power button assembly and install a new button with the battery in-place.
Works great now, although my mute button was also misbehaving (prior to opening the phone!), but I wasn't confident about removing the last ribbon cable required to get at that when I wasn't sure exactly what was wrong with it.