tbh I think you need to get a proper electrician on the job. Most light-switch operated extractor fans continue running after the lights are turned off, which suggests that the light switch activate a relay and the fan is on a separate spur (if it ran directly from the lighting circuit you'd expect it to cut out when the lights were turned off). OTOH, whether using a dimmer will fail to trigger that relay will depend on its properties, and I think that's where you need to get someone who actually knows what they're doing to look at it - otherwise you're just guesing and hoping, and that's a BAD IDEA (TM) when it comes to eletricity.
I'm pretty DIY competent but there's a couple of things I won't touch, and electricity in a bathroom is right up near the top of the list. If you don't know any electricians ask one to come round for a quote and watch his face when you suggest swapping the light switch for a dimmer - it'll probably give you a good idea of what kind of job it is