IR Remote, use a relay to send on and off pulses
Fundamentally, you need more than one device to control this system. You actually have 3 states, not 2: "send an ON command", "send an OFF command", and "send nothing". If you were to send the OFF command continuously whenever you weren't sending the ON command, it would be very wasteful of battery power. 

So you inherently need two logical control bits and two switch devices to control the IR transmitter. As Andreja pointed out in comments, there might be lower-cost alternatives you could use instead of relays.