Not that I'm saying you should throw caution to the wind, but being exposed to something containing asbestos is not inherently hazardous. It's not like it's radioactive or something. The hazard comes from the fact that the asbestos has to be inhaled where, depending on what type it is, it can lodge in your lungs.
I dare say that handling a wire made with a sheath of, for example, some encapsulated chrysotile asbestos, poses very little, if any, health hazard.
It's certainly a far cry from the WWII ship builders who were exposed to enormous quantities of airborne crocidolite asbestos, which unfortinately caused a variety of serious heath problems.