There are wireless headsets which receive a radio broadcast from a central transmitter. Such headsets are marketed for use with PA systems. They are handed out to hard-of-hearing people in the audience.
If you want two-way conversations there are inexpensive walkie-talkie systems that are worn on the head, with attached mic. These require that you push a button to transmit. Only one can transmit at a time. Everyone can hear whoever is transmitting.
For hands-free operation I believe there is a kind of earphone which delivers sound, and also picks up voice somehow. You may find a walkie-talkie system incorporating this.