Transistor system like a shift-register?
You will not find a shift register component with a free connect switch type output. An open collector transistor output will also not always work in a row/column switch matrix which normally requires switches with free ends. 

So I would recommend that you start with a normal shift register such as the 74HC595 to provide the control I/O signals from your microcontroller. The wire the shift register outputs to the switch enable pins in a component such as the 74HC4066 quad switch type part. This part offers switches with two free ends per switch that you can easily wire into the row/column switch matrix of the remote control device.