Check out this statute, which covers the property -- including dorms -- of any university (public or private) as well as K-12 schools:

(4) It shall be a misdemeanor for any person to possess or carry, whether openly or concealed, any BB gun, air rifle, air pistol, bowie knife, dirk, dagger, slingshot, leaded cane, switchblade knife, blackjack, metallic knuckles, razors and razor blades (except solely for personal shaving), and any sharp-pointed or edged instrument except instructional supplies, unaltered nail files and clips and tools used solely for preparation of food, instruction and maintenance on educational property. Any person violating this subsection shall be guilty of a misdemeanor and, upon conviction thereof, shall be fined not more than One Thousand Dollars ($1,000.00), or be imprisoned not exceeding six (6) months, or both.

Scissors that are "instructional supplies," or that are used solely for "instruction and maintenance," are excluded, but what about other scissors? Or anything else with a sharp point or an edge? Yow.

Or that's what S.C. Code § 16-23-430 suggests:

It shall be [a felony] for any person, except State, county or municipal law-enforcement officers or personnel authorized by school officials, to carry on his person, while on any elementary or secondary school property, a knife, with a blade over two inches long, a blackjack, a metal pipe or pole, firearms or any other type of weapon, device or object which may be used to inflict bodily injury or death.

Not is especially likely to inflict death, not has a substantial chance of inflicting serious or great bodily injury (terms that are indeed used in other statutes), not is usually used to inflict injury, but "may be used to inflict bodily injury." I say it again, yow.