I work at cable manufacturing facility and I can't say I've ever seen a shielded ribbon connector before, all of them I have seen are typically "plastic". Would it be possible to use connectors with a couple extra pins and attach the ribbon cable shield to those pins? Those pins could then be tied into your device grounds on each end. That would shield the majority of your conductors but you'd still be able to pick up interference at the connector pins. Maybe a metal shielding can of some sort to go around the connector housing on the device?
You could also use shielded RJ45 connectors and Ethernet wire potentially, if you are willing to use more than connector per device. Or another option you could look into would be micro-D connectors and use some shielded cable and backshell. Similar pin outs to the larger D-sub connectors but in much smaller packages. Link to some popular ones below.
http://glenair.com/micro_d/pdf/b/solder_cup_metal_shell_connectors.pdf