One of the frustrating parts of repairing older appliances is finding the right wire, especially power cord. Old ones very rarely survive in safe shape; most new ones look plain wrong.
For power cords, Sundial Wire has the answer. You've seen their work and haven't noticed it, in films and TV shows. They have very old-fashioned twisted-pair power cord...that just happens to be hiding modern insulation under the cloth.
Wiring up a classic radio or a telephone? Building retrotech from scratch? Check out the "Wire" listings under "Components" at Radio Daze; they have solid and stranded cloth-covered hookup wire in several sizes and many colors, including "pushback" solid, plus multiconductor cable and tinsel cord for telephone handsets, headphones and old-fashioned speakers. They have their own line of parallel-wire cloth-covered power cord and matching plugs, too.
Antique Electronics Supply has cloth-covered magnet wire in #24 and #26 size, plus Litz wire and cloth-covered hookup wire assortments, some power cord, cloth-type "spaghetti" insulating sleeving and #12 square tinned busbar.
Not Esoteric enough? Try the all-cotton-insulated wire at Jupiter Condenser Co. --And if you just have to have waxed-paper condensers, why, Jupiter's your only source of new ones, as far as I know. (The latter are not inexpensive but feature manufacturing techniques far superior to the old type; they've a line of modern Mylar fixed condensers as well). I have not done business with this company -- but they look interesting.
(Also stumbled over general-line/audiophile supplier Parts Connection, worth adding to your do-they-have-it? resources).