Recommend you check with Philly police or a Philadelphia gun rights attorney. I suspect CCW laws might apply. Minors may not possess CCW licenses in all states I am aware of.
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Ask the local police or a criminal defense attorney. You might also ask at your Kendo school; they may have had this question come up before. The wooden sword will probably not present problems, but a real sword may get you arrested. Remember also that merely carrying the sword around is NOT the same thing a waving it around, especially if done in a threatening manner. That will get you arrested every time.