Steve,
I've had a look at the handbook again and I think what you have is basically a PIANO. The SPLIT POINT on your CP88 is to enable you to have one VOICE to the right of the Split Point and another to the left.
On our keyboards, the SPLIT POINT is specifically to have VOICES on the right of the split (although you can have a Voice to the left of the split if you want), and to have Rhythms and Backings (ie. STYLES) on the left of the Split Point. These Rhythms and Backings follow the harmony of the CHORD you are playing with your left hand (so you have to play chords with your left hand). It's this CHORD played on the left of the split that you can set up to do ONE FINGER CHORDS, usually for beginners who don't know how to form the actual notes to make a chord.
These One Finger Chords don't produce chords with the LEFT HAND VOICE, only the harmony of STYLES that are triggered (which is why I mentioned in my post that on a keyboard you can't use a Left Hand Voice if you are playing in One Finger Mode).
Now I don't think you have any STYLES on your CP88??? In which case you won't be able to do One Finger Chords, as they only apply to STYLES.
Hope this helps.
Hugh