Don't rush to patent it, Dr Bill. Many cafés (naff caffs) in Europe use salt cellars with a hinged plastic top that do precisely this.
Hey, RodW maybe you could get together with Dr. Bill and arrange to send him one!?
Also, Dr. Bill, the shakers (!) for salt substitutes, like Mrs. Dash herb mixes (salt-substitutes) have a plastic cap that can be removed for measuring out larger quantities. Perhaps one of those caps would fit your salt shaker.

of troy :
Enlightening definitions.That said, I have some crystal salt dishes with a spoon - what is defined in the list as a table salt cellar. Now I know the proper name! Cellar not dish.

It well may be - as jmh said - that the confusion, in part, is due to local usage. I hear both cellar and shaker used interchangeably here in New England.
I will try to be a good girl and use the correct terms from now on while staunchly resisting the temptation to correct my friends!