Whatever source you have found as "1941" appears to be in error.
Little Valley, Cattaraugus County, NY has been open since 1822 per the post office listings on Jim Forte's website.
Also, here is part of page 830 of the 1907 "U.S. Official Postal Guide" listing the offices for Cattaraugus County, with Little Valley as the county seat and 2 rural routes (the "ch" and the "2" portions of the listing)
