I'm not sure I agree with the 90% humidity figure, but the sentiment is right. It seems to me that it is far better to concentrate on sucking the humid air out in the first place then spending money on paint that is mould resisting.
Since your fan is big enough as an aperture and in the right location, the next question to ask is whether it is actually sucking. You could test this with a smoke test from a taper. You might also want to get a handyman to clean out and check the ducting as it gets filled with dust.
I use Ventaxia fans, which I reckon are one of the best.
Lastly, if the fan is working properly, it may not be the best idea to also keep the window open since what then happens is colder air is sucked in from the outside, rather than warmer but less humid air being sucked in through the door from other parts of the house.
Warm air has a far greater capacity to hold water vapour within it than cold air.
What you are trying to do here is remove the water vapour laden air completely out of the room by sending it up the extractor before it gets the chance to condense out as droplets on the room surfaces.