This leather is called shammy leather.
"Big People and Little People of Other Lands" by Edward R. Shaw
The article known, in commerce, as chamois, or shammy, leather, is also called wash-leather.
"A Treatise on Domestic Economy" by Catherine Esther Beecher
Mine wasn't a leather purse, nor yet it wasn't a shammy leather, nor yet it wasn't one of them sealskin kind of things.
"Frivolities" by Richard Marsh