as a minimum, I would change the duct to an insulated one. the roll at about £30 is I think 10 metres long (the height of a house) so an ample amount. You can keep the rest for the next fan you do.
If you are paying somebody to do it, I would myself prefer to bite the bullet and get a (much) better fan installed, wired to the ceiling rose so it can have a run-on timer, and get the whole job done for years to come.
The fan you have is a very cheap one, low power, and noisy. With age it will become even noiser and you will want to change it. The power is less than I would want for a room with showers. You may need to leave the fan running constantly, which can be annoying as it is noisy.
A very good fan, with enough power to cope with several steamy showers a day, and including a run-on timer, is this one It has three times the extraction rate, and is quieter. It is bigger, so it is fitted in the loft, preferably on a thick ply board, spaced off the loft floor with a layer of carpet underlay or similar to deaden vibration. unsurprisingly it is more expensive. you use a bit more of the duct to run to the hole in the ceiling, where you put a decorative plastic grille.
Fans are usually fitted by electricians, who can wire a timer model so it turns on with the light switch, and runs on for a preset period to clear residual steam.