I gave this a lot of thought and it can be done with an action. I tested this and it does work for me.
Make a new blank file the same size as the largest image. Make four layers, on each layer make a rectangle for each side in the dimension you want to remove and fill it with a color. (top, bottom, right side, left side) Doesn't matter where the rectangle is placed on this file.
Name and save the file as a psd. (I called it crop.psd) Close the file.
Open one of the target images.
Start recording a new action as follows:
Open the crop.psd you just created
highlight the bottom rectangle layer, select all-copy-deselect
Paste the selection in the target image
highlight that layer and the background layer and align to the bottom
Go back to the crop.psd and repeat the copy/paste process on the target image for each side (top-right-left)
align each with the background layer to the correct side (top-right-left)
Close crop.psd
On the target image combine all the pasted layers into a single layer.
Ctrl+click the combined rectangle layer to make a selection, then invert the selection.
From the menu bar Image - crop.
Flatten the target image.
Stop recording.