A lot of you are very active with WVCDL so may be able to answer this question better than others I have asked to included Sheriffs and Prosecuting Attorneys

Are edged and impact weapons (Saps, Slapjacks, Batons etc legal under the law with the constitutional carry bill?

I work in a courthouse and have asked some trusted Sheriffs deputies and the county prosecutor and their stances are either probably or I don't know.

Yall shed any light?

A look at the exact law and how it is written is required but Google got me this tidbit:

"As of May 24, 2016,[3] West Virginia became a constitutional carry state. Any person 21 years or older who is legally able to own a handgun may carry the weapon concealed without the need of obtaining a permit"

By that it reads "Handgun".

I don't have the code reference handy but if you are over 21 and can legally possess the weapon you can carry it.  Switchblades, swords, bazooka, whatever you want as long as you are not prohibited from owning it. The issue with anything other than a handgun is that various cities have their own laws/ordinances about them.  Handguns are the only "deadly weapon" that has preemption.