There is no part number. As indicated, we make them up one at a time, from components any good bike shop has. This requires a high quality stainless woven inner cable with a preinstalled "Barrel" on one end. To keep the other end from fraying, once the length has been determined, we tin the last half inch with silver solder. Electrical solder with resin core will not work. You must use an acid flux and silver bearing solder, not lead.
The outer jacket should be the teflon lined type.
Perhaps you could get the bike shop to duplicate the entire cable by showing them your old one. They make cables from stock components all the time.
Remember that no cable, no matter how good, can stand up to misalignment or poor installation for long. The operating end must be able to swivel in the carburetter linkage and the open end of the jacket must be "aimed" correctly at the lever to be actuated. You also need to pay attention to the cut end of the jacket so that there are no sharp edges which will tend to saw away at the new core. You can do this with the core out of the jacket using a jewelers file or a Dremel type tool if needed. I find that cutting the outer jacket to length neatly requires a Dremel tool with a cut-off disc so as not to crush the spiral wrap and reduce the end opening. After cutting this way, the teflon has usually melted a little and it's necessary to get into the end with a nice sharp Exacto #11 blade to recarve everything nice and smooth. Sounds time consuming, doesn't it?
It is, and our cables, well made and properly installed, are far more expensive. But, they don't feel notchy, and they outlast four or five "storebought" parts. We think it's worth it, and so do most our customers. But it is a choice, and the commercially supplied cables will give reasonable service if careful installation is practiced. It is worth noting that in most cases, the problems seem to arise with custom adaptations, like the Weber downdraught.
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon