Yes, mono input = BRN (pin 3). If I'm reading the schematic correctly, using both the brown and the blue inputs (pins 3 & 5) will also keep the second output alive. I know you don't need stereo in, but for the price of one wire you can have a second mono output. If so, just tie BRN and BLU together at the PCB and connect those to your delay's output.
Green (pin 2) goes to ground.
You can clip the yellow and orange leads (pins 4 & 6). They inform the CPU whether there's a plug in either or both of the inputs, and probably mute the side without a plug. Clipping them will keep both sides always on if my guess is correct, there's a pull-up on the PCB through R81 and R83.
What to do with the black lead (pin 1) depends on how you're powering the Boss PCB. It provides the ground to the power section when there's no 9V plug in the power socket. If you can say more about your power scheme, someone can advise.