Although the plastic coated wire /might/ be better... the standard cord should be fine. I have several lamps here with the original 50+ year old cord...that are still fine.
When you replace the cord you might as well put on a polarized plug and ensure the lamp switch is on the "hot" side and the bulb tip goes to it.
Did you apply for a permit to rewire this lamp? It may take 2 or more presentations before the town board or HOA before they'll even consider voting on this project.
Where will you source the new wire from? Will you be using an approved vendor? Will 52% of the business be conducted with a minority and/or women owned business?
How will you dispose of the old wire? Have you completed an environmental impact study?
Who will perform the actual work? Is that person or persons licensed in the jurisdiction granting the aforementioned approval? Are they insured for the maximum possible damage that might occur if something goes terribly wrong during the rewiring?
Do you carry an umbrella policy to cover yourself for damages not caused by the contractor but that occurred as a result of this undertaking? Can you supply proof that the carrier of this policy has the funds to actually pay the full amount of the coverage?
I think you have a lot of work to do before you go out and buy any wire.
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