W.C. Fields died on Christmas day, 1946. Fields was horribly ill the last 2 3 years of his life. Hence, the recording Les supposedly played for Fields had to have been a disk-based system.
More likely, this story is NOT TRUE -IMPOSSIBLE. Les' signature multi-track sound was not possible until he acquired his first MAGNETIC TAPE machines. I was a neighbor of Les. I am a HAM, EE and a Jazz guitar player. PLUS, I am a BIG fan of Fields. Les would surely have told me about Fields' quote.
Urban legends fascinate me...
E.g., Urban legends like the one about Abraham Lincoln getting into a duel and requesting sabers as weapons; —pure fallacy. Never happened. But, this stuff is somehow is uttered, imagined, believed and then taken for truth.
Before you believe incredible things, do the READING OF REAL BOOKS YOURSELF. READING BOOKS IS A GOOD THING. Too many people learn what they know from "he/she said". This is not a good learning method or way to record history.