Hello Averil,
Henery Skillicorn bapt Lonan 30 Oct.1743 was the son of Philip Skillicorn & Mary Garret who marr. Lonan 22 June 1735.
I have his father Philip Skillicorn as Philip "of Laxey" as given in a Deed of gift in 1745 by his father Thomas Skillicorn of Skinscoe d.1750 (mother Joney Quay d.1733). Philip's brother Thomas was the eldest son (marr.Elinor Moore).
Henery was another younger son but he and his eldest brother John (b.1736) were named in the 1795 will of Isabel Goldsmith who was the wife of the second eldest brother Thomas (b.1738) as John and Henry Skillicorn, uncles by the father's side. This was the Henry who probably married Catharine Kermod.
[Sorry was writing this when Lois posted her far more comprehensive reply, but will post it anyway.]
Sue