I'm going to throw the cat into the pigeons now and propose the use of a file.
A cutter may dig or wander whereas the file is easier to control. It will easily follow the line and the cut can be made more progressively than with a blade through pressure control. Results may be
constantly checked with subtle compensations made as you either push or pull.
I'd clean a metal thread this way and see this as being no different. I frequently file wood in joinery work to achieve final accuracy.