I have some experience in the justice system. With an item like a hawk you have to consider not only what the penal code says but more importantly the reality of the justice system. Unless the penal code specifically adresses the carrying of a "hawk" or "tomahawk", you could very well be vulnerable to the interpretations, prejudices, and ambitions of cops, prosecuters, judges, and maybe a jury.
There is far more to the justice system than what is written in the penal codes. Sometimes cops make mistakes, sometimes they have bad attitudes, and as a result, innocent people can go to jail. People can sit in jail for days, weeks, even months while their situation gets sorted out, even if they are completely innocent. Prosecuters are ambitious and look for any chance to convict people, especially if there is a "weapon" involed. Many judges are so callous that they just don't give a sh*t wether you're innocent or not and will let you rot in jail while the system slowly grinds onward. It's not at all uncommon for innocent people to sit in jail, often because they either can't afford bail and/or they got stuck with a really crappy public defender who couldn't care less about them. It's a simple fact of life that innocent poor people often get screwed over by the so-called justice system. It's important to remember that first and foremost, the justice system is a BUSINESS. It's jobs, careers, paychecks, county revenue, and that great evil, POLITICS. Actual "justice" is often an afterthought.
Where I live the penal code says it's legal to openly carry a fixed blade. So I have no concerns about doing so. However, with an item like a hawk, if you are having an unlucky day, you might find yourself having to explain and justify to cops, prosecuter, judge, jury why you are carrying it. You might say it's a tool, they might say it's a weapon. You might say it's no different than a hatchet, they might disagree. And since THEY are the ones with the power to put you in jail, you deffinitely want to consider what THEY might think.
If the penal code isn't specific on the matter, and if you're not willing to consult with an attorney, I for one wouldn't risk carrying it. It might not be worth the potential hassle.