Jeffs approach is similar to what I described, with the exception I am under my house and Jeff is above it. Same idea though. One suggestion if you did this. Consider putting a smoke detector in whatever space you put the fan in. And mark your calendar to change its battery annually. You might also put a camera of some sort down there that you can access remotely.
Can't blame you for not wanting to go out a brick wall. I wouldnt want to do that either. But adding extra hose/pipe to get over to the window shouldnt be an issue in terms of the overall length if that helps. Especially if you are using smooth walled pipe, the distance you describe should be fine. For what that is worth!
900x600 80watt EFR Tube laser from Liaocheng Ray Fine Tech LTD. Also a 900x600 2.5kw spindle CNC from Ray Fine. And my main tool, a well used and loved Jet 1642 Woodlathe with an outboard toolrest that helps me work from 36 inch diameters down to reallllllly tiny stuff.