What is up with your magnet fetish? Mechanical watches have been mostly immune to mag issues since the 50's "The German DIN 8309 defines a mechanical watch as antimagnetic when its daily rate isn't changed by more than ± 30 seconds per day after it has been exposed to a magnetic field of 4,800 A/m (Ampère per meter)."
That is way more than any magnet you are apt to come into contact with unless you are 1)operating/having a MRI, 2)Work in a power plant, 3)around other large, extremely powerful electro magnets. Almost no rare earth magnets can produce fields of that strength.
The likelihood that your spiral spring would be magnetized by any magnet you normally come into contact with is not even worth considering.