can't use serial since the other device (video switch) has just an IR Receiver...
In that case just just figure out the timings for each signal you want to send (uSecs) and write a script to toggle a digital output pin on your Arduino. Remember it should be inverted.
In the target device you would have to think about making the connection at the output of the IR receiver. Either disconnect the IR receiver or design in some sort of LOGIC OR gate to isolate the 2 signals from each other.
You haven't explained why you cannot use the existing IR. If it is in another room you can get IR repeaters/extenders etc. or connect 2 Arduinos via RF.