Hi Bill,
Yes, very much along the lines that you are thinking.
The shield is there to ensure the cable can perform at its specified speed at its maximum length (295 ft for Cat 5 or 6). For short hops this should be far less critical, unless you happen to have a very strong source of EMI nearby.
The problem is that while the twisted pairs (signal conductors) in an Ethernet cable are terminated with transformers at either end, providing perfect galvanic isolation, the shield is not. So the shield could potentially transmit any noise on the ground plane of your switch, or anything it is galvanically connected to, to the DAC. While the likelihood is small we advise customers to use unshielded cables just to eliminate any possibility.