Hmmm, there are a few criteria you need to decide on before you can get into a design.
The ones that come to mind are:
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How automated do you want this to be? D o you want to just stick the blade in a jig, and have the gadget do all the moving around of the sensor? Does it do a mix of automated and manual operations to gather the measurements?
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How precise do the measurements need to be? Tenths of an inch? Thousandths?
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How many measurements do you need to take? And how fast?
A friend of mine has a CNC router. Router bits vary in length, and may not get chucked in exactly the same position every time. He puts a grounded aluminum block on top of the workpiece, and clips a wire going to a controller input to the router bit. His software slowly lowers the router until the circuit is closed, and then knows that the tip of the bit is exactly the height of the block above the workpiece.
You could do something similar, with a leadscrew-driven carriage travelling the lenght of the blade, and another leadscrew extending the conductive probe until it contacts the blade.
There are lots of projects on the web for doing (fairly) precise positioning from which you can get examples of how to build the leadscrew mechanism and get position feedback.