According to 28-1202 a CHP holder can still carry a concealed weapon that is not a handgun as long as you fit within 1(b), but it is only an affirmative defense and not under any of the terms and allowances of a permit.
28-1202. Carrying concealed weapon; penalty; affirmative defense.
(1)(a) Except as otherwise provided in this section, any person who carries a weapon or weapons concealed on or about his or her person, such as a handgun, a knife, brass or iron knuckles, or any other deadly weapon, commits the offense of carrying a concealed weapon.
(b) It is an affirmative defense that the defendant was engaged in any lawful business, calling, or employment at the time he or she was carrying any weapon or weapons and the circumstances in which such person was placed at the time were such as to justify a prudent person in carrying the weapon or weapons for the defense of his or her person, property, or family.
(2) This section does not apply to a person who is the holder of a valid permit issued under the Concealed Handgun Permit Act if the concealed weapon the defendant is carrying is a handgun.
(3) Carrying a concealed weapon is a Class I misdemeanor.
(4) In the case of a second or subsequent conviction under this section, carrying a concealed weapon is a Class IV felony.
