Another idea ... a defined length of that wire with a defined tension (wheels and weigths ) give a diameter related resonating string
It's always nice to convert a problem to a counting one 
Oh, I forgot about tension... I was thinking do it without stress, using the material's elastic modulus and mass to set the resonance. See:
If the density and elastic modulus is consistent, the wire could be secured between two rigid points and its mechanical resonance measured. This could be done in continuous motion with some difficulty.
That makes it even worse.

So then what, do it between two tensioners? Man... the sources for error are beginning to boggle the mind on this one. Okay, nevermind this, then.

And I would try a 4 point resistive approach.. just out of curiosity
That's not actually bad. Obviously, it still depends on material properties: temperature, composition, stress state (work hardening increases resistivity), and that your probing length is consistent (or measured simultaneously, to get a ratiometric measurement).
Note that you cannot get a perfect cylindrical electric field, because you can only make point contact to the side of the element. At best, you get a circular contact from probes all around, but this gives a cone shaped electric field at the end.
The length of that cone (or for a single point, a more blobby field shape, or any other superposition of them), will be dependent on the width of the wire. You must solve for this field in order to get the correct equivalent length. Even if the contacts are a meter apart, a 0.01% accurate measurement requires 0.1mm accuracy on those contact points! The diameter is much more than this tolerance, therefore the field at the contact points must be known, or calibrated out!
By the way, you definitely wouldn't use mercury for a continuous, surround contact: it will inevitably wobble and bounce with the wire's motion, moving the point of contact; and its resistivity is ten times that of iron, so you are actually making the electric field condition that much worse! (Nevermind the risk of contamination.

)
Tim