I was thinking, could this possibly come about in a world where the Naval Treaties come about as being more generous, with either larger tonnage allowances (and no limits as to how you spend your tonnage in detail), and with no post-WWI Doolittle trials to validate naval air strikes.
I was thinking this might be a curious and almost conservative way for the various navies to dabble in carriers, testing their effectiveness and all of that without the full liabilities of a carrier should the whole flightdeck thing not work out?
As for designs...
Perhaps a catamaran design, two gunship hulls on either side, and a flightdeck as the structural 'bridge' between the two gun hulls? That said, I can easily see this being...problematic, on account of needing (nonexistent) storage space under the flight deck to stow and refit aircraft, so perhaps a trimaran design would be more appropriate. But looking at such unconventional designs means some POD in naval engineering and design... And I don't know nearly enough of this aspect to see how to do it/whether it is even plausible in the early 20th century. Of course, you could also go with the CF design listed, but I can't imagine it being terribly effective without some (significant) issues in regards to room to make sure everything isn't just thrown together in the centre of the ship, per the flight cruiser plans in the wiki link.