hi muppetatwork - how did you proceed? When I read your post I thought it was mine!! I have exactly the same issue in exactly the same bathroom. Last night I spent some time discussing my problem with chatgpt. I worked out that my 4 inch (100mm) extractor fan is nowhere near enough to clear the room. Like you I then started looking at inline solutions and came to the same question as you - i.e. boxing the fan on an external wall. I'm tempted to re-core to six inch because the performance jumpp is massive. I'm pretty confident that it will stop, or at least hugely reduce, the humidity. When I have a shower (I'm a five min max kind guy) I can see it hanging in the air. Chatgpt said the bigger inline units are used in gyms etc to clear the humidity. I reckon it will work for me.

