Unfortunately, while the Casio and Yamaha "one-finger"* methods do agree for major chords, they are quite different when it comes to the minor, seventh, and minor seventh chords:
Major = The root key (Casio)
Major = The root key (Yamaha)
Minor = The root key plus any one accompaniment key to the right of it (Casio)
Minor = The root key plus the nearest black key to the left of it (Yamaha)
Seventh = The root key plus any two accompaniment keys to the right of it (Casio)
Seventh = The root key plus the nearest white key to the left of it (Yamaha)
Minor Seventh = The root key plus any three accompaniment keys to the right of it (Casio)
Minor Seventh = The root key plus both the nearest white and black keys to the left of it (Yamaha)
Casio and Yamaha both have additional chord-fingering methods-- although the ones which are available may vary depending on the model-- but none of the other methods can emulate the "one-finger" method.
On the other hand, some of the "normal-fingering" methods-- where chords are played using their actual notes-- can usually identify a particular chord even if you drop one or more "unnecessary" notes of the chord. The specific notes (if any) which are considered "unnecessary" or "optional" will vary depending on the chord, since you can't drop a note that would make the chord's identity ambiguous-- e.g., you might be able to drop the fifth, but you wouldn't normally be able to drop the third, since that would make it impossible to know whether you want a major chord or a minor chord. Anyway, it might be possible to find some "abbreviated" normal-fingering chords which are the same on both models.
* I don't know why these are commonly called "one-finger" chords, since you must play two or more keys for the minor, seventh, and minor seventh chords. More properly, Casio calls it "Casio Chord" fingering, whereas Yamaha calls it "Easy Chords" fingering.
