Starting with NE 28-1201 for the definition...
(5) Knife means:
(a) Any dagger, dirk, knife, or stiletto with a blade over three and one-half inches in length and which, in the manner it is used or intended to be used, is capable of producing death or serious bodily injury; or
(b) Any other dangerous instrument which is capable of inflicting cutting, stabbing, or tearing wounds and which, in the manner it is used or intended to be used, is capable of producing death or serious bodily injury;
Then we have the prohibition in NE 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.
The same as with firearms, I have not seen any prohibition on Open Carrying a knife.
Could the scenario you describe be considered concealed. Yepp. Far less concealed weapons have resulted in criminal charges. Disclosing it does not negate the act.
Screwdriver? IDK. Probably not. Then again, it probably depends on who you are and what you look like.