Possession is quite legal. You do not need a gi, dobook, or any other martial art uniform or even participate in a martial art class.
You only need to be able to show that they are used for the purpose of training or competing in "athletic" events. By it's very nature, the statute is ambigious.
As I have seen, so far, most officers aren't even aware of the fact that they are "illegal". Not even the Title 13 instructors at ALEA knew that back in the day. It was quite funny when a rookie wanted to charge a gang banger who had them in his posession during a fight, and the FTO didn't believe him that it was a violation of the misconduct involving weapons statute. To this day, the only time I have seen a person charged with a prohibited weapons violation for nunchaku was when they were used in the commission of a crime. Even then the county attorney wouldn't press charges under the statute, but instead charged them with aggravated assualt.
I know the statute specifically names the nunchaku as being a prohibited weapon, but it clearly states that it no longer becomes a prohibited weapon when possessed for the purpose of "training" or "competition". This is similar to the open carry law. Title 13 states that it is illegal to carry a deadly weapon, but then later in the statute it provides a defense to this by saying "as long as the weapon is wholy or partially visiable". I'm sure that you would agree that AZ is an open carry state, would you not? To understand this, you need to look closely at the wording in the statute: "Subsection A, paragraph 3 of this section shall not apply to a weapon described in section 13-3101, paragraph 7, subdivision (e), if such weapon is possessed for the purposes of preparing for, conducting or participating in lawful exhibitions, demonstrations, contests or athletic events involving the use of such weapon." The use of the words "shall not apply" is the key here. This means that the criminal statute for nunchaku possession is UNENFORCEABLE when it is posessed under the vague conditions of the exemption. Presently, I cannot find any case law or statute that defines what is required for "training", "competing", or "atletic events. The burden of proving that the possession of such a device DOESN'T fall under such an exemption is the burden of the prosecution.
Now, to contrast this with other statutes which use similar, but different, approaches to defining illegal and legal behaviour. Look at the justification for use of force statutes. It clearly says that it is illegal to use deadly physical force. Rather than claiming the statute doesn't APPLY for self defense, it provides a legal defense for such conduct should you be charged. This will require that you show that your actions fall under the use of force defenses, not exemptions.
Many of our criminal statutes are like this. They specifically say something is illegal, then later say that there are exceptions to those illegalities.