Kenmore Elite Refrigerator Door Pinched / Broken Wires
There are a lot of splice methods, but most of them aren't going to allow the wire to flex and will probably fail very soon if they are flexed.  For the splice method, I say whatever is easiest for you to accomplish in the limited space available is best.

What I will recommend is that you make two splices and leave solid wire in the area that needs to be flexed.  In other words, make a cut in the wires above and below the area that needs to be flexed and make your repairs in two spots that don't need to flex.  Use a wire made for flexibility - even if you have to use the same color for all connections.  Finding a good flexible wire is better than trying to match colors.