I re-certified as a Texas CHL Instructor on November 14, 2001. This question arose in class with the legal representative of TX DPS (Dept of Public Safety, our "state troopers").
The young lady came unglued when the student pressed the question and fairly yelled at him that CHL is a Concealed
HANDGUN license! (Stress was hers!)
She went on to explain that the CHL extends only to handguns covered by the license, i.e. SA=semi-auto and NSA=non-semi-auto).
She put a rather large exclamation point on it!
If you want real irony, even Bowie knives are illegal to have on or about the person. Jest don't seem raht, do it!