It turns out that the lady Batman is asking to be quiet is actually Catwoman in her first appearance. Thanks to my copy of Batman Chronicles Volume 1 (which reprints Detective Comics 27-38 along with Batman #1), I was able to read the story.
The question is, is this an actual panel or has someone manipulated it and played a trick on us?
The story dealt with Batman reading about a ritzy yacht party that was in the party. He figured every crook in town would also know about it and it would be a giant target for trouble. He sends Dick Grayson undercover as a steward who becomes suspicious when he sees a shady looking guy escorting an old woman with a sprained ankle. Robin discovers a crumpled note the man tried throwing overboard signed by "The Cat" and soon, the yacht owner's half million dollar necklace has been stolen!
The boat is soon boarded by other crooks but they're too late as the necklace has already been stolen. Robin takes them on and soon Batman arrives. What ends up happening is after the crooks are defeated, everyone is gathered at a costume party on the yacht when a fire alarm goes off. Batman notices the old woman running off and that she has "nice legs for an old woman!"
As they try to take the Cat away, she jumps overboard. Batman and Robin make their moves to go after her but bump into each other. Robin accuses Batman of bumping into him on purpose. Batman just comments on it being a "nice night." He also wonders if he'll bump into the Cat again.
In other words, there is no explanation why on Earth Batman said "Quiet or Papa spank!" Maybe Batman just liked giving spankings. It was the 1940s. Batman was attracted to her. Perhaps we should just leave it at that.
