Sometimes one might consider purchasing 'old stock' (be careful with this category of stock) silk-wrapped replacement cord for old lamps , or newly manufactured silk-wrapped replacement wires , so as to replicate the original wiring of such items .
Having seen many 1920-1940 electrical lamps thru the years , I've often found that they've been 'rewired' to function , but not always in a safe manner , esp with plastic light socket assemblies that are not really rated for the wattage that the original ceramic socket assemblies were .
Another point to consider checking is/are any paper or plastic 'tube or floral' elements in these old little fellers , such as used to imitate a candle , foliage (& etc) .... sometimes they do dry out & become friable & flammable (esp the ones made from celluloid !) .
Cool little item there , Bradley (and great advice from members) !