Since its a ribbon cable you can also use a braid of the same dimension I guess.
With normal cables you leave the wire in contact with the braid exposed a bit, then do a solder joint and fold it back over the insulation and then put heat shrink on top of it, I don't think you typically solder to the braid itself because its thin wire and it can break from deformation, unless your really careful and have good strain relief.
If you do the above method then the insulation of the cable is pressed into the soldered joint and the heatshrink is firm so you have good strain relief around the soldered area, unless you have a real connector that uses a collet.
Not sure but you can maybe put a harder backing plate out of plastic in between the cable and the joint to firm it up and offer strain relief, perhaps with some double sided tape.
Make sure the solder does not flow under the insulation where it can crack, leave enough braid exposed so there is a non-soldered fold to the junction.
What I can't answer is how to use heat shrink in this application without a backing plate, since it will fold the ribbon cable. I think you need one. Or maybe two to make a sandwich.
I would ask for a vibration test to be conducted since its pretty weird.