I presume you meant traditional, rather than ceremonial?
Huntingdonshire is part of the ceremonial county of Cambridgeshire*, and is a district in the non-metropolitan county of Cambridgeshire too. The traditional county (which included most of Peterborough UA south of the Nene) ceased to be an administrative/ceremonial entity in 1965 when it was merged with the Soke of Peterborough (which was split off Northants in 1888), and then that situation lasted 9 years before it all became administered as Cambridgeshire.
The traditional county does indeed have only electric services stopping on the National Rail network (Huntingdon and St Neots stations are the only two) - though the Nene Valley Railway exists. I presume we're not counting heritage! I don't believe there's any other traditional county, save Clackmannanshire, that only has electric trains.
*To be fair, there's zero reason why England can't use ceremonial counties to recreate traditional counties like Scotland does - it even splits Stockton UA in two so that the ancient boundary of the Tees is restored! There is therefore zero reason why Huntingdonshire can't be a ceremonial county. Sussex and Yorkshire can be treated as one should they want. 'Metropolitan Kent', Barking/Romford, etc don't have to be of Greater London for the purposes of person wearing tights and instead can be grouped with the counties they were administered by until 1965 should they want that. Though as a Bucks native, Berks can keep Slough - we offloaded it for a reason!