Replacing the battery in Vagabond II power supply

This is a long shot, but I hope someone in this forum can assist. I have a Vagabond II power supply and the original battery is about shot. I was thinking about replacing it with the smaller, lighter lithium battery used in the Vagabond Mini or something similar.

Anyone tried this? I'm powering a couple of White Lighting Ultra 1200 units, if that makes any difference.