I have no experience with that seller (in fact I have only bought one item on e-bay). Things to do with a battery extender:
1. Check your polarity (reversing the polarity will destroy the Z's charging circuit)
2. Check the voltage output. 4 NiMh cells will have a voltage of approximately 5.34V when not under a load. The Z asks for 5V. The difference should not damage the Z's circuitry. I have been using homemade battery boxes for several years.
The batteries you are asking about should work fine. PM me if you want any additional information and I'll try to help. I have a bit of knowledge gained through experimentation, asking dumb questions, ham radio apps, and scouring the internet. I can supply quite a few details that you will probably never need to know, but I like answering questions.
V-Man