The TSA (US) has just announced an easing of some of the restrictions for carry-on items on flights.
In addition to small folding pocket knives, sports equipment such as ski poles will be allowed in carry-on baggage. Ski poles are nearly identical to hiking poles, so presumably hiking poles will also be allowed.
In order to fit into carry-on luggage, hiking poles might have to be disassembled. They will unscrew at the “joints” into several shorter pieces.
Remember that for the Inca Trail, hiking poles must have rubber tips. These can be purchased in outdoors/camping stores where the poles are sold.