Can you get into the loft space above the bathroom?
If so you’ll definitely get better results with an inline unit like the one above. You can run some flexi duct from a 4″ grill in the ceiling to the fan, and vent it out of the soffit.
It’ll be more powerful, quieter, neater and will save you having to core drill a 4″ hole in the bathroom wall.
And you`ll get an ice cold airblast constantly like in our 2 bathrooms vented this way 🙁
New build, vented out of soffit facing prevailing wind direction, looks like there are no back draft shutters installed, so its freezing in both of them 🙁