I notice it tends to require re-application when doing a Century....

I usually use a q-tip. I've never noticed any fibers coming off of it, and even if some did I doubt they would cause any real loss of performance. I also always wear nitrile gloves. While not excessively toxic, most grease or lube is definitely not good for you, and it can hang around on your hands even after washing up. But I always worry about these sort of things as I work in a lab with solvents and other hazardous chemicals every day.

I remember having some bad-a$$ wheel bearing grease in the 80's that had lead or something in it. I tried not to ingest it or smear too much on myself.