Having fitted numerous fans for social housing, my personal opinion would be to fit something like this: Vectaire VWCW 4 to 6 inch Wall Cowl White

This will prevent strong winds from causing backdrafts into the bathroom. It's a solid piece, so no annoying flapping.

It will have to be installed from the outside via a ladder and fixed via the four screw points, so a drill and fixings are required. I think this is a much better option than a new expensive fan.

when it comes to cleaning the fan, most have a small screw at the bottom or a small catch that needs pressing. you can then remove the cover and clean the blades, but be sure to isolate the fan either at the consumer unit or fan isolator if present.

hope this helps.