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You may find building regs require the fan to operate with the light
switch.

I've never heard of any type of pull cord switch other than the
standard item.

However ISTR the new 17th Ed wiring regulations permits conventional
wall switches in bathrooms, provided they're rcd protected - assuming
separate switching meet the BR on ventilation.

Another alternative is a moisture sensitive extraction fan.

Best solution for the fan is a ceiling mounted passive infared and just a
single pull switch for the light.