Hi,

According to the image in the ifixit Harman Kardon Esquire Mini Battery Replacement guide, the battery in your device has the following specifications:

3.7V 2000mAH 7.4Wh with the dimensions of 6.5mm depth (or height) x 52mm width x 52mm length. (P655252)

I am unable to find an exact replacement battery, however the closest one that I could find is this one, which you may wish to consider.

It has the same voltage specification of 3.7V, but has slightly less capacity at only 1800mAH. Its' dimensions of 5.0mm x 50mm x50mm means that it will physically fit into the device.

Hopefully this is of some help.