Shouldn't need an adapter. Looking at the picture in the linked posting, both ends are female. The airbrush-side coupler is smaller, certainly, but it's shaped like a hex nut, not a threaded tube. If you have the same product, it should work out of the box (bag).
My air hose works as you describe - the actual coupler is a threaded sleeve that secures the steel tube that caps the hose to the brush/compressor. There's a rubber O-ring inside to form a proper seal, while the sleeve keeps the mating ends compressed together, stably. There's some play in the sleeve, so it can collapse nearly flush with the end, when unattached. Unless you see threads on the outside, though, you're fine. I'd trust that a Badger hose is designed more sensibly than what you fear.
[edit: typo]