Joe,
Looks like simple flexible wiring conduit, commonly called Breezes. Most likely tin plated copper braid. More for physical protection than EMI shielding, although that would be an added benefit. You could send each conduit out and have a exact copy made, or send out the entire turret harness together. Harnesses and conduit are hard to get right the first time unless you have done it before, not to mention the expense of the tools required. A restoration shop would have these tools and expertise already and would get a bulk discount on conduit, plugs, wire, etc.
http://www.airflexindustries.com/ has the conduit. An AIRCREWMAN'S GUNNERY MANUAL from 1944 would have a lot of info you need about operation of these turrets.
Are you planning on having the turret working? If not you could skip the associated wiring and just install the empty conduit for show. You might not want to run those turrets on the ground anyway. Although it would be quite the crowd pleaser, you would have the danger of hitting or pinching a spectator with the quickly spinning turret. Is this the Erco 250SH front turret? It had a self contained hydraulic system didn't it? If you got it to work, I suppose you could limit the speed somehow. I think the side turrets have hand cranks but the front and rear turrets had a hand operated emergency hydraulic pump to move the turret if the electric motor running the pump failed. You would have to run these on ground power or the little Homelite APU that these aircraft had, so you don't wear down the aircraft batteries. Amazingly there is a lot of info and manuals on these turrets still out there.
Good luck on the restoration and I'll be watching your progress.
Keep Em Flying,
Craig Hoaglund