Tim,
Both of the Sharp versions and the Baring Gould one should now be online in The Full English. Harriet Young's version has the crew as 920 and as you say gives no mention of Nelson.

The most likely scenario here is that it was written by a broadside hack using names current at the time, but probably based largely on an earlier ballad which would take some hunting down. Collections of naval ballads like Firth, Masefield, Ashton might turn something up.