How can I output to one of 4 different outputs without using a demultiplexer?
Use a 7400 Quad Nand gate, use your microcontroller to set one pin on each of the 4 Nand gates (you'll need to use 4 outputs of the MCU). Into the other input of the Nand, you provide the Inverted data you'd want from that output.

Or provide the 4 control bits (not the data, but the control) using 4-bit shift register or 2 packages of dual D_FF the 7474. You'll need MCU outputs to provide clock and data. You will also have glitches in your de-muxed outputs.