Bathroom ventilation - no windows & limited access to exterior walls

Hi, I have a ventilation problem in the bathroom of a ground floor apartment. I discovered the extractor fan in the ceiling is not connected to the outside and is blowing into a small (circa 3 inches) cavity between the ceiling and concrete slab. There are no windows.

I had been considering running ducting to the outside in the ceiling gap, but the cavity is too small and with the metal frame that the ceiling plaster is attached to, it would not be possible.

The obvious solution would replace the ceiling fan with a wall mounted fan and run ducting along the top of the wall where it meets the ceiling and vent to the outside. The only trouble is, it would run through the bedroom and would look awful. However, I have not ruled this out, but am wondering are there any other solutions.

I understand that recirculating fans are not great and only get rid of odour, whereas I'm more concerned with moisture. As there is a hotpress and water tank next to the bathroom, would it be possible to use an extractor fan and blow it into ducting in the hotpress and into the watertank or back into the waste outlet of the bath? If the ducting does not run outside, when the ducting fills with steam would the steam be pushed back into the bathroom through the fan? I might have answered my own question here, but would like to hear from someone that knows this area or any other suggestions appreciated.

Regards

N