SWMBO has decided an above-the-range microwave is to replace existing range hood.

The hood circuit powers other equipment and cannot be used for the microwave. This is a code restriction, not a practical one. The only option is to "move" the existing microwave outlet to the cabinet above the stove, probably 6' away from existing location.

Local codes aside, it it generally acceptable to use armored cable or some other form of mechanical protection to extend the circuit (outside the wall) to the new location? Aesthetically it's not a problem. Fishing wire through walls isn't a good option as cabinets, firewalls and exterior walls are in the way...not worth it for a microwave relocation.

Then there's the extension cord method....