There is a referance on manx notebook;

"SKILLICORNE, a name peculiar to the Isle of Mann, is puzzling. It is most probably derived from a local name now forgotten, beginning with the word skellig, 'rock.' We have Skellig and Cornaa separately among our local names, but not in combination.

CORNI is found as a personal name in the Landnamaboc, and SKYLI in the Flateyjarboc.

Sir Philip SKILLICORNE was a vicar in 1521.

[Skylyngcorne 1428] SKYLYCORNE [1511], SKILLICORNE [1521], SKYLLESKORN [1540], SKILLICORN [1650], SKILLECORN [1651].

Maughold, Andreas, Lezayre, Malew (c), elsewhere (u)."