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How easy is it to replace the whole length? That would be the best option. You can join it with a maintenance free method, easiest is wago connectors in a wago box. As long as you can squeeze a little extra length out of it to get the ends joined in the box. You have compromised the inner and outer sheaths so I wouldn't recommend just taping it, on the other hand if it's your home then you just have to yourself to answer to and tape would stop the electrons leaking out! It is supposed to have 2 protective sheaths though.
If it runs from back box to back box and you can pull a new wire easily, do it that way.
I've nicked the edge of a mains cable. The cable inner is undamaged. Can I cover in self almagating tape or heatshrink or do I need to replace the whole length?