40W soldering iron will produce too much heat for delicate soldering.
I assume you are trying to shorten the trunk cable. Cut about 10 pieces of small sleeving (10mm long x 2mm wide sleeving) for the small conductors and about 100mm of the larger sleeving to cover the whole cable when done.
Put the large sleeving over the trunk cable. To keep the large sleeving away from the cut, scellotape it to the trunk cable.
Now for the individual coloured wire: strip back the trunk's outer sheath to expose about 15mm of multi coloured wires.
Strip 2mm of insulation from each coloured conductor (you see 2mm of exposed copper, 13mm of insulation before the wire disappears inside the unexposed trunk).
Tin the 2mm of exposed copper on each coloured wire. Wait for it to cool before putting on your 10mm small sleeving that you prepared earlier (you now see each coloured wire with 2mm of tinnned conductor then 3 mm of coloured wire then 10mm of sleeving).
On the opposite end of the cut, strip back about the same 15mm of the outer sheath. Tin 2mm of conductors like you did before. You are now ready to solder.
Use the thinnest tip you have for your soldering iron. I think a 15W or 25W soldering iron is ideal for small wires. Wipe the tip on the wet sponge then melt a tiny bit of solder onto the tip of the iron tip.
Line up each colour so that the two ends overlap by about 1mm. It's useful to have a friend holding the two wires for you. Use the melted solder at the tip to heat up the join until the two ends fuse together. Leave the join to cool. Proceed to the next wire.
When all the wires are done and cooled, push the small sleeves over the joins to insulate them. Test the electrics next. When you are happy, heat the small sleeves with the side of the irontip to shrink them.
Remove the scellotape, slide the large sleeve over the cuts and shrink with the side of your irontip.
