I don't think that kind of attribute can be copied/pasted. I'd recommend converting the shape to a symbol and then using the symbol. That way you can update all the linked instances any time you like. Unfortunately, it means you will have to scrap your existing shapes (save 1). Hopefully you aren't too far along in your design.
if your other icons are the same shape you could reduce the opacity of the others to around 50% and then place the originally skewed one under each icon and skew it until it matches - you could align a couple of guides to the skewed one to make it even easier to line up
I tried with a bsic shape, not sure if it'll work for you. Make the skew (transform) open the History panel, select transform and save as a command. Select next object and use command