New York Knife Company was actually a two-fold company. The original company was actually based in Matteawan, New York and was founded in 1852. It produced knives under that name. In 1856, it merged with Walkill River Works and moved its operations to Walden, NY and started producing economy knives under the logo "Hammer Brand" starting in 1880. In 1928 all knives they produced bore the factory name of Walkill River Works, which were made until 1931 when the company folded. So, by this history, your knife could date anywhere from 1852 to 1880.
...... at least this is the history as I have it.