You can’t rerun the extraction through Image Extract because it will flatten againt white and extract again…. which would look terrible on the edges.
Hpowever, you can create an action to load the transparency as a selection and to crop to the selection.
Control+clcik on the layer will make a selcetion of the transparency. Then do an image>crop in the PS menu.
If you record those 2 steps in a n action you can then run a batch on the action through Pixnub Hot Folder and save as PNG.