The coil wires on these pickups are incredibly fragile and it's very easy to break them and/or the attachment points of the actual shielded cable. I'd actually suggest just snipping the existing single core shielded cable through the yellow casing ~5-10mm short of where it's stripped, then carefully separate the 3 parts (core, bare to coil, and bare to baseplate). Make sure you'll be able to insulate the bare to coil wire with heatshrink and, if you can, then attach some new 2-core shield wire. One core to each of the snipped coil wires and the shield to the baseplate.
I did this type of procedure on a PBG humbucker, snipping and attaching new cable, and it worked well. If you look carefully in this image you can see my new green wire is connecting to what was the original bare wire coil connection. I slipped some heatshrink over the original bare wire so it couldn't short with anything once it was all buttoned up.
Topped off with more heatshrink before adding some more tape around the coils and sealing it up.
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