You should be fine using only one cable.

I have a HSU STF-3 with L and R inputs. I tried using a Y adapter and could not detect any difference in output using an SPL meter. I also have no problems with auto power on using a single cable.

The only reason for the left and right inputs (AFAIK) are for systems without a dedicated sub output that have line out ports (or integrateds with jumpered RCA jacks between the preamp and power amp where you can insert Y adapters between the L&R channels and the power amp. A full range signal gets sent to the sub and you'd use the sub's crossover.

The signal received by both ports is summed, which should have a net zero effect as you are sending the same signal to both jacks then summing them.

Hope this helps.