then the wall will be rigid enough
put it close to the ceiling
it looks like above you is another flat, so you will not want anything too noisy or intruding through the ceiling. If theirs is a bathroom, and/or they have a concrete floor, noise will not be such a nuisance.
Modern extractors with ball-bearing motors can be surprisingly quiet
A 4-inch/100mm fan is usually the minimum, and is adequate for a bathroom or WC, but not if you have steamy showers. They usually are rated at about 80 cu.m/hr. I recommend you have it wired to the ceiling light, with a run-on time delay. ("T" for "timed")
If you only get a 100mm, you may have to run it for long periods to keep the bathroom free of condensation. It looks like you have solid 9" brick walls, which will be cold in winter.
You can get a 125mm or 150mm fan that will be substantially more powerful. You are going to have to core a hole through the wall anyway so you may as well do a big one.
If you get one with a noise rating of 25db, that is pretty quiet.
Some are available with speed control at much higher cost.
Soler & Palau make the best ones I've seen, but some of their identical models are branded Envirovent which is the UK subsidiary, and often at lower prices. Read the tech spec to ensure the motor is mounted on flexible rubber pads, and has ball-bearings (other, similar-looking makers do not have these features and their fans are not as quiet). I have also used Airflow, which are not quite as good, and Manrose, which are much worse.
Here are a few examples. Look at air throughput, in cubic metres per hour, and sound, in db
100mm
125mm
150mm
You can get ducted ones that are even better, but they are usually fitted in a loft or false ceiling, being bigger.
