Ok... so nobody answered my question.
I went ahead and tried to replace the battery anyway.
So, just in case anyone with the same problem finds this forum via Google, I'm going to answer the question myself - hopefully it will help someone.
Writing as one UTTER newbie to another, here's how I changed my Spykee battery. Those of you who are mechanical geniuses and too clever to reply to such basic questions might like to read it too, just for a laugh (or a reminder of how it feels to be an utter newbie).
1. Open Spykee. Four obvious screws on the bottom, four not-quite-so-obvious up a bit, hidden by the treads. Take the treads off to get at them.
2. Remove the base carefully, because there are various fragile wires connecting the main body to the base you've just unscrewed. I *suppose* you could unplug these, but I found I didn't need to. Just be careful not to put too much strain on any of them.
3. See the battery? Ok, just exchange it with the replacement. Easy, huh? Well,
that's what I was expecting, but alas, NO. You WON'T see the battery. I sat for a silly length of time thinking, "OMG! NOW what do I do??? Where IS it?"
4. Actually it's buried deep. I don't think the manufacturers intended us plebs to mess with this. First you have to unscrew the motherboard thingie. Four screws.
5. THEN you have to unscrew the plastic panel UNDER the motherboard thingie. You'll finally see the batteries.
6. Changing them is easy enough, once you get to this point.
7. Reverse the steps to put Spykee back together again.
And that's all there is to it.
