Get a piece of plastic or wood and create an oval covering for the booths exhaust vent, then cut a 4" circle in the covering. Stick a 4" collar into the 4" hole.
Then use polyurethane expanding glue to secure them together. (Polyurethane glue holds almost anything and expands into any gaps you might have)
Then stick the dryer hose onto the collar, securing it with a worm clamp and some duct tape. (Using the collar & worm clamp will allow you to remove the hose, if needed, in the future.)
Finish it off with some silicone caulk to seal it up completely.