Getting into the machine and, more pertinently, putting it back together again could be the most awkward bit. Razors tend to snap together and when you manage to unsnap them it's not always clear where all the bits go and in what order when you come to reassemble them. (And that's assuming you manage to track down all the bits from the far corners of the room....)
As for the battery, I wouldn't mind betting it's a NiCad. They never last all that long in razors- I think it's to encourage you to buy a new one.
Do let us know how you get on though. As HS93 says, if you can get into the thing you should be able to upgrade the battery. Make sure you keep the voltage the same though - you wouldn't want to lose your nose and ears.
