Replace mechanical switch with transistor? MOSFET? Relay?
Without knowing the exact details regarding the circuit connections that the switch was connected to it is not possible to give a generic answer as to what semiconductor components could replace the switch.

What you can do though is to select a relay that has contacts with ratings similar to the switch. Ratings being the current carrying capacity of the contacts and the open circuit voltage rating of the contacts. And whether specified for AC or DC service. 

With the relay in place you can now control the relay coil as suitable to your remote control system and be totally isolated from the device which is being switched.