SC,
I have several dolphin robots and to be honest I can't tell much difference between the ones with the swivel and the ones without it. They both seem to tangle about the same. And, the contacts in the swivels get corroded over time and have to be cleaned or the robot does not get any power.
That said, if I were to buy a new cable today, I'd most likely get the one with the swivel..
I suggest that you call Marina Pool and Spa and ask them which cable would work best for you.
Not sure if you have disconnected your current cable for the motor box yet. If not, you should, as the problem may just be a corroded and broken connector right where the cable connects to the box. I've seen the pins corroded so badly that they are no longer usable.
Thanks,
Jim R.