I would "lap-solder" ** the individual wires, with offsets in the splice points so there can be no shorts between them even if your added insulation fails, and heatshrink each wire, then heatshrink the whole cable joint. If you fill the final heatshrink with dielectric grease before performing the shrink, then it will also keep out water pretty well.
** My version of lap-soldering is different from typical.
Typically, you'd just strip a bit of insulation back on each wire (perhaps 1/4", tin the conductors, overlap them with insulation in opposite directions, and solder. This makes a straight wire spliced in the middle.
I strip about 1/4" back (for thin signal wires, about 1/2" for stuff like phase or battery wires). Then I slightly spread the conductor strands apart on each end, and push them together (imagine sticking two brooms together, sweepy-ends into each other) so the strands overlap. Then "roll" the strands together, so they are held together by each other's strands. Then solder that.
In either case, you slip the heatshrink tube over each wire before you do the splice, and put the big cable sized heatshrink over either of the main cable sections.
