I can't visualise how the two ends of the wires are located, but is there any way you can arrange it so that the wire is drawn over a pulley or past an idler wheel during the loading process, so that you can measure how long it is by counting revolutions of the wheel?
this is very similar to the machine we have, although ours will be a lot older proeff.de/htm/en/html/ProductsProduct_InformationTWISTER.php
there is a video on that page of a different model but the idea is the same, except its the operator will be pulling the wires tight.
one of my first ideas was to have a loop of cord running the entire length of the bench and back round pulleys at either side, one that has an encoder on that will count revolutions that can be used to work out distance. then all the operator would have to do is when loading in the wires in pull the cord at the same time as he is pulling the wires tight. the problem is that the cord might get in the way and tangled up in the wires and there would have to be a way to reset the count after every time.
Some people have used a 1D LIDAR, but that tends to get kind of expensive. You could also have the user pull out a tape measure and have a camera read the number of the tape (Obviosly not with an Arduino, but with a PC or RPi it could be done).
LiDAR sounds interesting but I bet health and safety would have a problem with lasers pointing at people. I think the tape measure and camera is a good idea but would be over complicated and well outside my skills.
I suspect a sonar sensor would work great. Soft things like clothing or fabric are usually excellent targets at short range (1-5 meters is fairly short). At this distance hard surfaces work well, but the angle needs to be perpendicular to the sensing direction or the sound will reflect off at an angle and miss the sensor. The soft targets will absorb some power, but usually the sensors have enough power to cut through that.
I defiantly think this is the way to go, there is nothing extra for the operator to do and nothing to get in the way.
any recommendations on what sonar module to use? how accurate are they?