I will add that you would need to make sure there are no shards of the armor sheath that could pierce the conductors inside. If it's open enough, you could slide a couple of "red heads", one on each side, or just one if that's all the room you have. Then do your tape job.In the middle of a run, I'd spiral-wrap with electrical tape, overlapping 50%, end to end and back. That gives you four layers.
At a cable end, I might slide some new sheath from scrap cable and just tape the gap where the old and new sheaths meet.