I might try to sleeve the cable with white woven sleeving and run it behind the leg of the mantle to make it less obvious. It was only £65.
I solved a similar problem with a metre long drill bit.
I admit this is very tempting, but I am loathed to take a drill to something that is "finished". I'll take a look at the potential exit/entry points and have a think.
@aggi started
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I might try to sleeve the cable with white woven sleeving and run it behind the leg of the mantle to make it less obvious. It was only £65.