Relay voltage spikes
There are 2 devices that can generate spikes.


The relay coils. The diodes in anti-parallel will help suppress the spikes when the relays are turned off (The stored energy in the magnetic field is converted back into voltage/current causing a spike that may be inductively and capacitively coupled back in to the mains). Assuming these are DC relays, feed by DC this could be a good solution But may still need filtering.
The motor of the fan and the contacts of the relays. Here the motor can be switched on at any point in the mains cycle. If the relays close or open when the maximum current is being drawn you have a similar situation as turning off the relay coils. (The stored energy in the magnetic field is converted back into voltage/current causing a spike that is conductively and may be inductively and capacitively coupled back in to the mains) The solution is to switch at the zero point in the mains cycle. +1 @Brain Drummond comment for devices to search for that can use Zero Point Crossing ( zero crossing switch, or zero crossing SSR (Solid State Relay) ) 


Keeping the current loops as small as possible and moving cables away from noisy circuits can also help depending on how sensitive the audio equipment is.

After that it is inductors ,resistors and capacitors to construct filters to damp any spikes left.