I actually ran the Z with 4 alkaline batteries before I got my NiMh batteries. I would not recommend doing this!!! I just got lucky. With the NiMh batteries, I watch the charging light. When the light goes off (indicating full charge), I disconnect the external battery pack. After a bit (time depends on what I am doing with the Z), I reattach the external battery pack until the charging light goes off. I have found that if you let the external pack and the internal battery go dead, the Z will shutdown very ungracefully and without warning!!
I believe I have a bit of information on the battery packs, voltages, and Z current requirements. Let me know if you want it. I don't have it with me (at work) but can probably still find it all at home.