Aye Steve,
I'm with Ken with using the brake cleaner after removing the nipple and shortening the inner cable. You can also buy brake cleaner in a 5 litre (1 gallon

) can and pour some into a tray and give it a reet scrubbing with a tooth brush, afore using the aerosol to flush.
Burning off the grease can affect the tensile strength of the wire making up the cable and if you don't rinse off the flux residues with hot soap and water the salts can be corrosive.
A big copper solder iron heated with a parrafin blow lamp is always good value (Eh, GC!

) But a gas blowlamp with the copper soldering tip is also good. Tin the cable afore trying to solder the nipple and if the cable won't tin then clean it again.
As with all these jobs, take your time, be methodical and you should be fine. A bit more blacksmith engineering (Fred Dibnah

) design, is good for thumpers!
Toodle pip, Bill.