Let me introduce you to the best pair of headphones for travel that I own:
Bose QuietComfort 20 Acoustic Noise Cancelling Headphones, Apple Devices, Black https://www.amazon.com/dp/B00X9KV0HU
They are $250, wired and have a small battery brick that is not replaceable that is charged by micro usb.
The newer one by Bose is one of those neck things and is $300.