I presume that you want the circuit closed when the button is pressed and the circuit to open when you take your finger off the button.
One way - use one of the simple FM transmitters that have been described here with an audio oscillator that is moderately stable. That's the transmitter portion. Use a low cost FM receiver at the other end and build a simple tone decoder - I recall one circuit that uses a 567 (I think, will verify) as the decoder - use earphone jack to connect to decoder. Output of decoder to close relay (possibly via transistor switch).
For more stability and reliability get a pair of FRS radios in place of FM transmitter and receiver - play tone via small speaker into microphone. Connect earphone jack on other to input of 567 decoder.
The use of the FM radio or FRS stuff isn't build from scratch but lifts some of the electronics burden until you've proven that this will work.
For more reliable control you could use DTMF encoder and similar decoder on other end. Lots of amateur radio stuff on this.