How I do it. The hubs uses this method when he takes things apart. First piece removed is farthest from the thinga majig. Often depending we both will take a quick photo.
As I take each part off the handle, I put it down in a "horizontal line" with the other pieces with the first one off being the one farthermost from where I am working. I usually pull each piece off and place it down so that I can pick it up the same way I put it down and put it back on the handle the same way it came off. Hope that makes sense. Oh and maybe put the pieces taken off from one side of the handle to the left (as you are holding the cutter just as you would use it) and the pieces taken off from the right side to the right. Hope this helps.