I once bought a solder pot but had mixed results with it. For one thing, it's not very portable and it's not really very safe to be carrying a pot of molten solder around. It's fine if you can make cables at a workbench, but sometimes you need to string cables through something on the bike and tin the end of cable that's at the handlebars or some other awkward place.
That being said I saw a good mechanic make cables on a bike using a hand soldering gun.
Soldering gun.jpg
I bought one for myself. They generally have a dual wattage determined by the trigger pull, and you'll want to use the high wattage.
I had a good degree of success with it making my own cables - until the last time I went to use the gun. I could not get the connection to hold for anything. It's a bit of an art; you have to splay the cable end and use some generous amount of flux for cleaning and heat transfer, you have to get the solder to fill the splayed end such that there is no way in hell it will pull back through the ferrule. At the same time I am told if you heat it too long the solder wicks too far up the cable and makes the cable inflexible and brittle in the area before the ferrule.
I probably am not using the write terminology, but on clutch cables there is usually a large ferrule that the cable feeds through, then if feeds through some smaller ferrule that you solder onto the end of the cable to prevent it from pulling through.
I think how well you need to do has a lot to do with the amount of stress placed on the cable. Clutch cables are the worst, maybe brake cables after that. Your cable doesn't sound like it will have to endure a high amount of stress.