I’m not sure if I’m missing something here, and I assume there’s a similar function in an Android Phone - I regularly “scan” odd shapes using my iPhone - I usually use photoshop to transform to the original shape, but you can use the crop feature in the phone to do a fairly good job.
Place the object on a square grid so that you have a reference.
Turn on “grid” on your phone and line it up as best you can with the square grid background. The phone has a pair of cross hairs (see the yellow and white crosses in the middle) that will align when it’s horizontal. Taking care to do that will eliminate most of the parallax error.
The crop tool has also three tools for rotation, horizontal and vertical parallax adjustments. Just fiddle until everything lines with the grid. It’s easier to do than to explain and I don’t have a grid to use in my hotel room! (I will do it with the bathroom tiles if this isn’t clear enough)
Then take the image and trace half of each side in your cad programme, and mirror each to get a perfect shape. Or just trace the lot if it’s not perfectly symmetrical to begin with.
For something like the job you are doing though, I would use a joggle stick (ticking stick) and whip it out with the bandsaw in less time that it takes to fire up the computer! 
EDIT - Couldn’t help myself - the same image before and after adjustment. Not perfect but this was an extreme example and I have a bus to catch!
