You could glue the dongle to the headphones.
https://www.hidizs.net/products/dac-cable
It's tiny, so it just becomes part of the earphone cable.
I have the Sonata paired with some 30 GBP Chi-Fi earphones in my walking-around bag, and a Dragonfly Red paired with some 130 GBP Chi-Fi earphones in my cycling bag. The bike bag can afford to carry the bulkier equipment!
Now i just need to get a motorbike or something, so i can logically justify buying a Dragonfly Cobalt and some really nice earphones ...