There are a number of ways to do what you want and then some.
Have a look at Copycat, there is manual for it in Member's Doc's and it will provide you with gcode file. The code can be backplotted to a dxf drawing if you have a program to do that.
It is used with a usb camera. Know nothing about Rhino so can't help there.
There is another program called Probe It and besides using for the lathe I "think" there is a version of it for the mill.
You must use Mach's original screen set.
Have you considered just taking a picture and importing into to CAD, scale it based on two dimensions, and just draw over it?
Easy in say AutoCAD, but again know nothing about Rhino.
A spring activated probe can be used on paper. You are just closing the switch so speak. Just something to think about.
I created a screen set for my lathe. I was interested in being able quickly get a profile or whatever with the option to do it a number of different ways and with different degrees of accuracy.
Selection depends on what you want in the end.
One of the quickest is to just get a few selected points and have those points drawn in CAD as points, a line, or an arc. It will not work with "all" CAD programs but works with the two that I use.
So one can put a figure in the machine, get some points, have it drawn, import the file into a program, output the code, and be ready to duplicate in say 10 minutes.
Just some thoughts on what you want to do.
RICH