Crimp splices
I'm a big fan of crimp connections ... soldering makes unnecessary stress risers where the solder ends in the wires. Crimping is way better.
If you don't need to take apart the spice, I'd use two MIL-S-81824/1 crimp butt splices with their heat shrink waterproofing/strain relief, with solder sleeves to connect to the shield. If you can tie the shield together with a short piece of wire (~2in or less), you likely don't have to carry the full shield all the way across (though some braid would do nicely to produce a good, full shield) A nice piece of translucent heat shrink over the whole deal, extending a few inches onto the wires would close out the job.