That would be a good trick! In my opinion, assuming the inner wires are not uncovered, I would probably go with self-amalgamating tape. You are basically trying to restore the integrity of the outer mechanical protective sheath.
Where did you drill?
I was told there are some cable jointing kits where there is some clamp thing which allowed you to use shrink on a cable without cutting the cable, but when the epoxy resin types came out this special went off the market. What is required depends on how much damage and also how easy to get to, likely best option is to leave it alone. But without pictures it is hard to tell.
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