Do you have reason to believe that the historical surname was not passed down to a son? Otherwise, pursuing matches with other surnames is rarely productive
Even if you know there was one, there is little you can do with the matches unless you can pin down the generation and place with DNA testing or a paper trail.
About all I would do is search your surname board with the matching surnames and vice versa to see if anything has turned up. NPEs are often documented in court orders of court minutes, few of which have been transcribed and indexed. VA probably has the most. There is a book of bastardy bonds for NC.