You can get Bluetooth transmitter/receiver units if you really like your current headphones.

I have a set of headphones I like that I use for ps/xbox/pc and handheld switch but when I found the playstation headset on sale for a decent price I picked up a set for when I'm playing docked. The USB dongle works plug and play with the switch dock, is recognised as USB headphones and activates the volume control on the quick menu. It is easy and effective, I just have to remember to charge them every now and again (something I'm not used to).

There are other models of USB headset that work but not all of them are compatible. If considering another model I'm sure you can find a comparability list somewhere.