Installing light switch that requires neutral wire - wire is continuous through box

You are in conduit, which changes everything.

Nope, you can't cut it. You don't have enough length remaining. Both stubs will be illegally short and you would then have to replace both of them.

However, what you can do is replace just one half of the run, left or right, whichever one is easier to fish/pull. Continue using the original wire on the other half of the run.

Identify which one is easier to replace by opening up both connecting boxes, and push and pull on the white wire from here. You will get tactile feeling on which one moves easier. While you're there, see if there is an abundance of slack in those boxes and you can just move wire around. The legal absolute bare minimum is 3" of insulated wire sticking out beyond the surface of the wall at each box.

Then on the "easy end" pull the slack out of the old wire, and lash it to the new wire with electrical tape at least 6-8", as long as you can. Streamline the "nose" so it doesn't hang up on things. Then, from this box, pull the old wire out, dragging the new wire in.

Shove the old wire down the other pipe back to center, because you probably pulled all the slack out of the other box. That box needs that slack. Then unsplice old and new wire, position everything and cut all the wires so they are 8" beyond the surface of the wall.

You could also leave the old wire and double back from the next or previous box on that conduit. I do the "pass thru and double back" trick all the time to reduce practical box crowding, but that won't help you here.

Since you will be making all your joins at a wire nut, you might as well use stranded THHN wire which is more flexible and easier to handle, there's also no stiffness penalty for #12 wire. Must be white or gray.

I am in the same position, Roger. I am not an authority on the NEC, but I have been researching extensively after reading Harper - Reinstate Monica's answer and I have to say there are other sources saying it is perfectly fine to use splicing to extend the wire to sufficient length to satisfy NEC 300.14. See, e.g.: https://www.facebook.com/mikeholtenterprises/videos/2721769841295232.

The code section 300.14 simply says there must be 6" of "free conductor" running from the entry point of the box, and for certain size boxes, at least 3" that extends out past the wall. But, does "free conductor" mean unbroken conductor? Well, I cannot find anyone (other than Harper - Reinstate Monica) suggesting that if a wire winds up being cut too short inside a box that the code requires completely re-running it from its source. That seems like overkill and makes no logical sense from a safety/engineering perspective, assuming the splice is done properly.

And if it doesn't require that, then there is nothing wrong with the OP's idea. He could simply cut the neutral wire as long as he adds sufficient length to both ends to satisfy 300.14.

I welcome anyone to correct me if I'm wrong here, but I think before jumping straight to running new wire that less labor intensive means should be considered, and citing published sources would be great too.