Unless Herman's nat papers have attached to it a certificate that the manifest has been found (this is not done on earlier naturalizations) than I suggest you assume that the ship name and/or the date of arrival is in error.
Also, do not limit your search for a manifest to NY. He may have arrived at another port (even through Canada.)
My grandfather and all his siblings arrived in NY in 1892. I have the passenger manifest. On their naturalization papers only one of them got the ship name correctly. One listed a name of a ship that hadn't even been built yet in 1892.
Have you searched for surname Wayler in records from Kovna (Kaunas)?
A quick search at the above site (using soundex search for the surname) finds variants such as: WELLER, VELER, FELER, etc.