Just wanted to let you know that I was able to connect this battery as the only one to my Z5500.
There are 4 wires: 1red, 2red, 3black, and 4black. I used 1red as a plus (positive terminal), 3black as a middle contact, and 4black as a minus (negative terminal); 2red is not used. Then I made a sandwich: "Fake" battery on the bottom, 3M mounting tape in the middle, and Sony/Palm battery on the top.
For the "fake" battery:
Using piece of balsa (for weight, can be found in a crafts store like Michael's or A. C. Moore), I made a "copy" (dimension-wise) of the original Sharp battery;
To reproduce the original battery's contacts, I pushed three U-shaped, 10 mm-long pieces of 24-gauge solid conductors (the only ones I have) into the wood.
Then, I ran the three wires under the Us and pushed the conductors further into the wood to secure the wires.
My Z works as it should with this battery for a couple of days now and it does not look bad aesthetically.