Hi Liz,
I think it was the right idea when you said you were going to order the birth registration indexes (on film at the MM Library, or on film through the Douglas LDS Family History Centre, or in the volumes at the General Registry) and check each district over a 3-5 year period for Catherine Cain, so that you can cover the whole of the Isle of Man looking for her birth. If you transcribe all the details for every possible index entry it will save you going back a second time if your first guesses don't work out when you look at the actual birth registrations. I would also note every Catherine birth (of other surnames) where the father isn't given, in case she was illegitimate but later known by her father's name, as was common in the Isle of Man.

Good luck, and let us know how you get on!

Sue