What kind of shifters? Indexed shifting (assuming you want it to continue indexing) = a home made splice isn't going to work. Actually, there are cable splicers that are used on bikes that have S&S take apart frames. They actually work without needing to be adjusted each time but that would still require buying an additional replacement cable plus the splicer. The fastest, easiest and cheapest way is to simple replace the cable AND THE CABLE HOUSING with new.

One of the things about modern derailleur bikes that amazes me is how precisely and reliably they shift tiny amounts of cable.