I just watched that episode of Leave it to Beaver last weekend. I made my older 30+ kids watch it because I thought it was the funniest episode ever. But the barber was not the one who played Floyd the barber on Andy Griffith unless they changed barbers somewhere along the way.
Now that you mention it, I think it may have been the episode where Wally gets a shave from the barber. I am certain the guy who played Floyd also played a barber in “Leave it to Beaver”.