I know today we have a whole range of wireless switches and relays, but is it worth it? I felt the same about my central heating system heating the DHW in the summer. No option for hard wires, did find a wireless tank thermostat, but it would cost around £100 so never bothered, I did spend a lot more than that in the end, and have an iboost+ which has a wireless connection to my meter box so uses excess solar power, part of the solar package, don't think it will ever pay for its self.
At £20 for one same as failed, so simple to fit, is it worth the effort to improve it? I found this bathroom no sign of mould even with no fan, but old house in Mold, that did have a mould problem, so I sat back an pondered why, and realised all down to a gap under the shower door, in Mold it was over the bath, so could not seal under the door even if I wanted, and when using the shower the thermals distributed the moisture through whole bathroom, here I have a shower room with no bath, and the cubical seals at the bottom, so moisture stays within cubical.
So if the old fan was good enough just replace it like for like, if it was not good enough OK then look for some thing better. Ideal to my mind is for the fan to activate for set time when light is turned off, don't want cold air circulating around the room when having a shower, one it gets me cold, and two it can draw the damp air into the rest of the room, it is when I have finished in the shower I want the moisture removing, when all that would naturally run down the drain has already run away and I only want to remove what's left in the air.
I know the fan if no opening window under building regulations needs a 15 minute run on, but it does not need to be powered by lights, in fact when the regs first came out you had to have a way to run fan without turning on the lights, but this was dropped, so a simple pneumatic push switch which the user can manually press is within the regulations, and you can opt to press it going in or out of shower.
But if the system works why change it?