Hi, I would actually caution against this. I'm not sure of the shielding configuration of the original cable, but I'm assuming it's a grounding braid, enclosing a ribbon cable. Is that right? You can buy shielded ribbon cable from good electronics suppliers. Usually, buying shielding separately costs a lot more, makes a lot more work, and usually gives a considerably inferior reault. One important consideration is the attachment of the shielding at one or each end (depending on the requirements of the design). The quality and coverage of the attachments can make a significant difference to the shielding factor. For some cables, the shield is also the primary ground conductor, which is critical for good signal integrity. If you are not experienced, achieving a high standard of shielding can be difficult and excessively expensive.
Does anyone have specifications for that cable, or even a photograph of an intact specimen? I ask this as I may be able to give more helpful advice if I knew more about the cable.