Here's what you do. Go to a big box with a good electrical department and look for RayChem or SolderSleeve butt splices, and some heavy duty heat shrink. I mean really heavy duty, not the stuff that sort of looks like in flattened tubes in the package. If it doesn't look like small black pipe you're looking at the wrong kind. Pick one that will fit over your cord and make sure it has pieces 4-6 inches long.
- Slide on the hard heat shrink. Use a nice, long piece, mayybe 4
- The splices have you slide on a heat shrink tube before connecting
the conductors. RayChems use a crimp barrel to connect the ends.
The SolderSleeves require you to twist the ends together.
- Connect each conductor (whether twist or crimp), then slide the
splice's individual heat shrink over the connect and apply heat. The
SolderSleeve splices will melt solder into the joint and also melt
some plastic sealant at each of its ends to environmentally seal the
spliced connection. The Raychem works almost the same except it uses
the crimp barrel instead of solder to join the conductors. It also
has a heat activated environmental seal.
- When you have all three conductors spliced, slide the big piece of
hard heat shrink down over all three conductors ahd use the heat gun
on it. That leaves a splice that's well protected from stress and
NOTE: carefully read the instructions before you begin to prepare the ends. The total length of the exposed conductors and their insulation should be something that the hard heat shrink tube will cover with an extra inche on either side. For example, if the exposed conductor insulation and their splices is two inches long, you should have at least four inches of hard heat shrink. You want that extra length there to provide a bit of stress relief for the cord so that jerking it around in-use won't strain the spliced connections.
I've found one or another of these splices at Lowes and Home Depot. The last time I found the hard heat shrink at Home Depot. Lowes probably has it, but I haven't looked there. Most big box home centers carry the spices and heat shrink.
If you don't see the brands I mentioned, take a close look at the splices they do have and you might see one with the same characteristics. The standard crimp splice kits (the automotive kind) are not something you'd want to use except breiefly in an emergency.