You could use a fabric cover like it is shown here:
This won't prevent dirt etc from accumulating, but you can wash it after exercising.
Instructions how to make such a cover can be found at https://www.instructables.com/Fabric-watch-strap-cover/
It's easy enough to apply a sticky tape of some sort, but even the best one won't conform to the surface of this complexity, and dirt will happily get under it.
I have very good experience with lining the inner site of a metal watch band with band aid
The glue is very sticky at body temperature and the fabric is flexible enough to bend with the metal watch band. It will prevent black from the metal to rub off on you, but like a fabric band, it will get dirty over time. On the plus side, this also prevents these tiny hairs from getting trapped in the metal band.
In my case this was durable enough to only be renewed about once a year.