Washington, Hawaii, and New Mexico are the only three states that don't allow balisongs. Hawaii's law seems to be the only one that specifically mentions them by name and they apparently fall under the switchblade/gravity knife definitions in the other two states. I hope Knife Rights has a plan to tackle these three states in 2019.
As far as shipping it into the state? Anybody can order a balisong online and have it shipped if the seller is willing to send it anywhere. The buyer would take their own risk with regard to the laws of the state they're in. But I've heard some say that selling balisongs over state lines may possibly violate the Federal Switchblade Act's clause on interstate commerce, so depending on who you ask, that could potentially be a law the seller would violate. That said, the interstate commerce clause with regards to switchblades is practically never enforced as several dealers sell and ship them across state lines all the time. Most of the time, enforcement only comes into effect when somebody tries to import a switchblade or balisong since customs watches that stuff.
This isn't professional legal advice as I'm not a lawyer. You'll have to ask someone who has the proper legal experience and expertise to help you with your questions here.