In general in the US there is no state regulations of any kind regarding edged weapons except for carrying them concealed, and certain municipalities have restrictions. Some state codes do classify things by blade length in terms of defining what they are.

So far as I know, there is no "license" to be had anywhere, of any kind, in the USA for a sword. Concealed carry permits are firearms only kind of things, and will not cover a concealed blade, at least in Iowa. Other places may vary.

Mostly it is up to the discretion of the officer on the scene who is responding to any sort of complaint that may have been called in what happens. The attitude and demeanor of the individual will play a HUGE role in that. Be nice, be polite, be civil, be reasonable. If at an event where such things are expected, it is no problem, usually. Walking down the main street wearing a sword could get you some unwanted attention, but there again, it is going to depend a great deal on your attitude and demeanor.