Let's say I have a coax cable with 83% velocity factor. I want to use
its inner conductor (that is solid copper single conductor) so I remove
the outer sheath and the braid.

I am left with the inner conductor and what was the dielectric, now
performing as an insulator around my wire.

What is the resulting velocity factor?
* 83%, as the original cable
* 100%, copper's
* something else?

As others have already mentioned, you have a bit of wire with a plastic
environmental sheath. You didn't mention the frequency, but for HF I have
each close to trees. The calculated length is about 4% longer than the the
actual length requred for resonance, even with more than 3 metres of nylon
cord to support the ends.

In other words, the velocity factor of a bit of wire in space is 1. Put it
near something and that VF falls a bit. Stuff it in a metal tube and it will
fall a LOT, maybe even approaching half (0.66).