Edge device connector port failure

I have an Edge 840, and when I went to disconnect it from power after a charge, the connector was frozen to the connector port. Because it was already charged, the device powers up fine, but closer inspection of the port revealed it is fried. Once this device loses its charge, it is forever dead.

Is it possible to wirelessly get my historical, un-synced rides off this Edge before I lose the charge? It shows it's connected to my home network but is not syncing the ride history to either my PC laptop or my iPhone using Connect. I'm hoping there's some way to retrieve this data before it dies for good.