Greg, you need to look at the Kk Michael parish registers on film. The IGI invariably puts an illegitimate child under the mother's surname.
My experience with PRs is that they don't usually put a surname for the child. They usually read "Charles illegitimate son of Margaret Boyd..." or "Charles the illegitimate son of Philip Kaighin and Margaret Boyd..." [and the latter would also be put in the IGI under Boyd]. There are sometimes other details, such as the parish of one of the parents if different from the one where the child was baptised.

Sue