At Engineered Cinema Solutions, we use Canare L-1.5C2VS cable and BCP-C1 Plugs, which are solder core and crimp collar for "spaghetti" type BNC. Outer diameter is approximately 2.9mm and I believe this is the thinnest cable Canare makes. Belden makes a slightly thinner cable at 2.5mm but I have found the Canare to be the best balance between flexibility, thinness, and durability. It's more economical than going with a custom cable maker too.
You will need a Canare TC-1 Crimp tool and the TCD-1DB die set for the crimp tool to crimp the collar, as well as a basic soldering station with a fine tip, and a bit of liquid flux. It starts to add up once you factor in all the tools required, but if you're making a lot of cables it's worth it.
I order my Canare supplies from HAVE Inc in Hudson, NY. They are fantastic there and always well stocked.
Hope this helps.