I think you would be ok ... except that all "weapons" are pretty much prohibited subject to allowable uses.
New Jersey prohibits "slingshots" by name [no differentiation between a David versus Goliath type and a wrist rocket.]
The origins of this goofy law according to legend are a legislator's attempt to prohibit something called a "slungshot" which is something like a "blackjack" which is a padded device holding a heavy weight used to bonk someone on the head. This particular statesman misspelled "slungshot" and ever since a slingshot has been considered a threat to society that can only be possessed by criminals.
How long does it take to become a "a pretty good shot with an atlatl?" :