All the Cavendishes I have found on the Island have been Corjeags in disguise. There are still a few Cavendishes here but the name Corjeag has died out.
Turning to the Ballaugh branch, my information is that John Cavendish who was baptised in 1813 was POSSIBLY married in 1840 to Mary Jane Hughes but this is unproven. Further research is required.
In Manx Cur Jeag means giving dish hence 'Cavendish'!? When did your ancestor migrate?