Thanks Ian!
I tried the following trick. I duplicate the layer then shift the top layer one pixel vertically. Then I add a transparency mask and select the one row rectangle and paint the mask. It's a bit of work, but it is not too bad.
I'll assume the blank pixels are at a fixed horizontal or vertical position for every given image size (small/medium/large). Since you state "row", I'll assume horizontal... Since the blank pixel row does not move, it's a perfect scenario for using Automation.
You should study the Automation topic, there are lots of lessons on YouTube that show how to create a small process that you can launch and will execute all the steps you execute manually.
Basically you record the sequence of actions you would do manually (you enter a record mode when you create a new action), then you save the sequence with a name and optionally you can assign the sequence to one of the f1--f12 keys.
Do a Google search with the following:
automating repetitive photoshop tasks
and you'll find a whole world of answers to your problem
Ciao from Massimo