Anything that has the Canon
name on should really come with some kind of warranty. I would imagen that their reasons for not providing a warranty is down to the type of item that it is. Cables tend to get pulled about and can break.
I expect you wish you'd wish you'd bought the third party one now.
If you bought it from a shop, I would attempt to take it back, or if it is an online retailer, call them and ask. Anything is better than nothing; and at least you can say that you've actually tried.
As for repairing the cable yourself, once the ^ above fails, you might as well have a go as you've got nothing to loose.
I have a third party off camera remote shutter release for £5, and the build quality is very good, I can't see the wire coming out any time soon. It is only a button at the end of the day though, something that can be repaired.
However if your cable is broken and the fault is the wire inside, it won't be worth even trying to repair. If the connectors have come out and you can open the cases either end, and you think it's just a quick solder job, then why not?
Good luck anyway