I'll have to hurry with this as I'm in the office and have work to do (but beng my own boss I can take a few minutes).
You say that you "believe" that John F (born 1881, Sedbergh) was your ancestor.If that's right (and it would be interesting to know the source of the uncertainty; we might be able to help) then you have a link into quite a family of Fishwick genealogists.I'm aware of at least six people researching a wide variety of "twigs" from this Sedbergh - Kirkby Lonsdale - Kendal "branch" of the Fishwick family.
John's parents were Seth Fishwick, originally from Casterton near Kirkby Lonsdale, who married Agnes Tebah (originally from Kendal) in 1798.To the best of my knowledge they had 10 children, and John was their 6th.He appears to have lived in Kendal for much of his life and had several children, including your great-grandfather John.I'm not quite certain, as I never checked carefully, but I think his wife was Mary and they their other children included Agnes, Rachel and Thomas.
I myself am descended from Seth's younger brother, Richard, whose son Thomas gave rise to most of the widespread clan of Fishwick hill farmers to the north of Kendal.
I hope that helps.If you want more detail, you can contact me by ordinary email and I can send you various papers for you to print out that can't (technically) be sent over a forum.