There is no reason to fear using your iBook G3 battery in your iBook G4. It won't harm it in the slightest (the battery or the iBook).
I have not swapped the batteries in mine simply because I work on the adapter nearly all the time, but I would not hesitate to swap them if the occasion arose where I needed to do that.
As a matter of fact, you do need to charge the iBook G3's battery from time to time in order to keep it functional. If you decide you want to store it, follow the procedure listed in this Apple article:
http://www.apple.com/batteries/notebooks.html
A stored battery won't last forever, though, so you'd just as well get whatever use you can from it while it is working.