Two shift register could work like the 74hc595, to pulse the correct device, and you could probably tie all the outputs together(maybe a resistor between just in case) to one input pin since your only timing one at a time and you would know which one is responding already
so that'd be 4 pins(one input, one serial out, one clock line, one output enable)
Since the Output Enable on the 74595 puts the outputs in a high-impedance state you will need a pull-down resistor for each of the outputs.
I don't think you can hook all of the outputs to a single pin, even with resistors. The one HIGH pin would be fighting the 11 LOW pins. You'd need a 12-input OR gate made from a couple of CD4072s or CD4073s.