Thematically, there being no overlap between the weapon skill and the Tenebrium skill can make some sort of sense when you realize that the skill is all about handling Tenebrium safely.

Imagine, if you will, a person who has both a water balloon filled with normal water and one filled with radioactive water. The person can be skilled with using the normal water balloon all he wants; flinging it, juggling it, etc etc, since there is no risk to his person. But the radioactive balloon requires more care, different techniques to handle properly without risking damage. A Water skill of 5 won't mean a thing if you're pulling your punches trying to use the radioactive balloon with 1 Tenebrium skill.

Conversely, the techniques used to handle the radioactive water balloon would have little effectiveness when handling normal water balloons.

The point I'm trying to get at is that the Tenebrium skill is like an exotic stance that all weapons have; it's not really compatible with how the weapons would be wielded normally if they weren't radioactive pieces of Rot.