I don't believe you will have a problem but, a few thoughts that may get you a quick answer:
1. Contact USPS, FedEx, or UPS customer service and ask them - they should know.
2. Ask your friendly neighborhood gun dealer. He should know and if nothing else, if it can't be shipped to you, he as a dealer might be able to take the shipment.
3. Check Cabela's, in their catalog and web sight, the section where they sell black powder guns I have seen lists of states that they can not ship to. If AZ is not listed you are probably good to go.
I would say call the local ATF office but, you would probably have a better chance of hitting the lottery than you will getting someone to answer the phone or return a voice mail (just speaking from personal experience - your local office may be a bit more responsive to the public they are supposed to be serving).
Cheer and welcome aboard mate. :thumbsup: