I can't find anything in the Arizona Revised Statutes nor the Tucson Code of Ordinances (since your location says Tucson) specifically prohibiting impact weapons. AZ state statutes mostly prohibit explosives, chemical weapons, and nunchaku, whereas Tuscon seems to have something against airguns and slingshots.
That being said, here are a few things to consider:
1. I'm not a lawyer, nor am I from AZ. While it's fairly easy to search through state and local laws online, there's always the chance that I missed something. I'll provide links to what I was looking at below so you can read things yourself.
2. Even if they aren't illegal, brass/metal/composite knuckles are quite stigmatized, especially among law enforcement. Even if they're legal, just carrying them could still get you in trouble if an officer is having a bad day and/or questions your motives for carrying them.
3. I wouldn't recommend knuckles anyway. Even the better-made ones can break your fingers unless you've trained with them and know how to use them.
4. Batons require training as well. As easy as it seems to just swing one around at an attacker, it would be all too easy for someone to grab. You'd need to train to avoid lethal hits as well, which is harder than it sounds. Batons are also harder to conceal given their size.
5. Impact weapons are just that -- weapons. You won't convince an officer that you're carrying a baton for utility purposes

. So if you do choose to carry an impact weapon, keep it concealed and only pull it out if your life is threatened and you have no other options. If you have to use it, even in a genuine SD situation, it's still going to be your job to convince the judge and/or jury that that it was truly your only option.
If you make the choice to carry an impact weapon, I'd recommend a Comtech Stinger. It's similar to composite knuckles in that it's a force multiplier, but it focuses all of that force into one point and should also be a lot safer for your fingers. Basically, you hold one end against your palm and the other end protrudes between your index and middle fingers for punching.
Links:
Arizona Weapons Law
Tucson Code of Ordinances - Just search "weapon" or "weapons" in the Quick Search box at the top and you'll be presented with links to the section of code that mention weapons. I tried searching for specific words like knuckle, knuckles, baton, impact, etc. but got no results.
Comtech Stinger