"Cran" was the usual Old English word for the crane. According to the 2nd ed. of Jamieson's Etymological Dictionary of the Scottish Language (apparently 1840), it survived for some time in Scotland as a name for the heron. Conceivably it survived here and there elsewhere, records for dialectal words often being less than adequate.

The OED affords no reason to assume that "fowling" ever referred to hunting anything other than wildfowl.

So if Jemmy originally went "fowling," "fawn" should be a later substitution.