I can't find anything in the docs or articles that suggests that is possible.

There is an article by Blake that shows how you can create live set entries that have your custom 'Touch Sensitivity Settings'.

https://yamahasynth.com/learn/cp-series-stage-pianos/cp-os-v1-5-touch-sensitivity-offset/

Then you can send a Program Change command to switch to your specific live sent entry.

Sorry - I don't have access to a CP to answer your question directly but others my be able to add additional info.

many thanks 

You would have to use SysEx to change the velocity curve.   Address (20,00,10) with value 0=Normal, 1=Soft, 2=Hard, 3=Wide, 4=Fixed.   If fixed, then address (20,00,11) would hold the fixed velocity value (1-127).

To change these values you would send a Parameter Change type SysEx message.

F0 43 10 7F 1C 08 20 00 10 02 F7

Where the "10" after F0 43 assumes device #0 which is the default and you would only have multiple devices if you had more than one CP keyboard chained together on MIDI and then you'd have to assign a device address to each of the CPs in the chain so you could differentiate.  The address would end up being "11..1F" depending on what you set the device address to instead of 10.  Bolded is the address tuplet for setting the velocity curve. Underlined is the value of 02 which is "hard".   Replace these values as necessary to do what you want.   The documentation which the above was lifted from is in the owner's manual starting at page 44.

This isn't what you were asking for since a SysEx is not a CC.  But given a CC is not available, this is the only other MIDI option to do what you're asking.  It may not help since some devices cannot deal with SysEx as easily (or at all) like they can control change (CC).