Prohibited weapons are mentioned in the state constitution?
When in doubt, see what the law says. In this instance, it's Title 18, Section 908, to wit:
18 Pa.C.S. § 908: Prohibited offensive weapons
(a) Offense defined.--A person commits a misdemeanor of the first degree if, except as authorized by law, he makes repairs, sells, or otherwise deals in, uses, or possesses any offensive weapon.
....(1) It is a defense under this section for the defendant to prove by a preponderance of evidence that he possessed or dealt with the weapon solely as a curio or in a dramatic performance, or that, with the exception of a bomb, grenade or incendiary device, he complied with the National Firearms Act (26 U.S.C. § 5801 et seq.), or that he possessed it briefly in consequence of having found it or taken it from an aggressor, or under circumstances similarly negativing any intent or likelihood that the weapon would be used unlawfully.
....(2) This section does not apply to police forensic firearms experts or police forensic firearms laboratories. Also exempt from this section are forensic firearms experts or forensic firearms laboratories operating in the ordinary course of business and engaged in lawful operation who notify in writing, on an annual basis, the chief or head of any police force or police department of a city, and, elsewhere, the sheriff of a county in which they are located, of the possession, type and use of offensive weapons.
....(3) This section shall not apply to any person who makes, repairs, sells or otherwise deals in, uses or possesses any firearm for purposes not prohibited by the laws of this Commonwealth.
(c) Definitions.--As used in this section, the following words and phrases shall have the meanings given to them in this subsection:
...."Firearm." Any weapon which is designed to or may readily be converted to expel any projectile by the action of an explosive or the frame or receiver of any such weapon.
...."Offensive weapons." Any bomb, grenade, machine gun, sawed-off shotgun with a barrel less than 18 inches, firearm specially made or specially adapted for concealment or silent discharge, any blackjack, sandbag, metal knuckles, dagger, knife, razor or cutting instrument, the blade of which is exposed in an automatic way by switch, push-button, spring mechanism, or otherwise, any stun gun, stun baton, taser or other electronic or electric weapon or other implement for the infliction of serious bodily injury which serves no common lawful purpose.
(d) Exemptions.--The use and possession of blackjacks by the following persons in the course of their duties are exempt from this section:
....(1) Police officers, as defined by and who meet the requirements of the act of June 18, 1974 (P.L. 359, No. 120), referred to as the Municipal Police Education and Training Law. [FN1]
....(2) Police officers of first class cities who have successfully completed training which is substantially equivalent to the program under the Municipal Police Education and Training Law.
....(3) Pennsylvania State Police officers.
....(4) Sheriffs and deputy sheriffs of the various counties who have satisfactorily met the requirements of the Municipal Police Education and Training Law.
....(5) Police officers employed by the Commonwealth who have satisfactorily met the requirements of the Municipal Police Education and Training Law.
....(6) Deputy sheriffs with adequate training as determined by the Pennsylvania Commission on Crime and Delinquency.
....(7) Liquor Control Board agents who have satisfactorily met the requirements of the Municipal Police Education and Training Law.
You will note there is nothing in there about blade length. The law does prohibit switchblades (press a button, the blade whips out), but that's about it. Swords, katanas, machetes, etc. are not mentioned nor specifically prohibited.
The police officer you speak of should research various SCOTUS rulings concerning rights before spouting off his erroneous opinions.