In the Irish language, "sean-nós" refers to a style of SINGING, rather than a type of SONG. That style does show a good deal of regional variation - just like the language itself! Partly due to tradition and partly due to the influence of competition (the term first appears in connection with Feiseanna around the end of 19C.), certain songs are strongly associated with the style and that repertoire is often loosely referred to as "sean-nós songs".

A native speaker of Irish would never refer to a song in English as "sean-nós", even if when singing such s/he used elements of sean-nós style.

Some elements of sean-nós style have, of course, transferred into traditional singing in English - and many of the airs have been adopted to carry such, making the use of ornamentation, for example, quite natural.

So, the idea of "a sean-nós song written in English " is not a particularly helpful way of characterising any song.

Regards