In terms of procedure, there are several options available to each committee. The committee could adopt a motion saying that witnesses can't testify without wearing their headset or if the headset they have has not been tested.
It's important to remember that witnesses are often called at the last minute, with only a few days notice. There's a complex process for confirming the appearance of a witness, sending the witness a headset, and all the other details. It can take up to a week.