I came across some interesting prop-related illustrations in a series of books called The Shakespeare Rare Print Collection, which was published back in 1900. The first shows a performance in progress on the stage of the Red Bull Playhouse circa 1672. I’m not really sure this is a Shakespeare play, since the drawing was made during the Restoration Theatre period well after his death.
You can see some minimal hand props, like a cup and a lantern, as well as plenty of swords and musical instruments. The picture shows a complete lack of furniture though, as well as any sort of scenic element.
The other illustration shows specimens of fans “as referred to in the notes on the Merry Wives of Windsor.”
This drawing was made in 1786. It is fascinating how much variation there is in such a seemingly simple hand prop.