I'ld like to switch on/off the Layer voice with the assignable FS. This would be the only purpose of the footswitch that I need. In the general controller menu (utility) I can't find that funtion.

How can I do that? Or is it simply not possible? Maybe with a trick?

There is no direct function to 'press' the Layer button by stepping on a Foot Switch - (why you do not find it.) Maybe with a trick... perhaps.

You can program the LAYER Part to follow volume control if you have the other pedal (the FC7 sweep pedal)... simply program the PERFORMANCE to include both the MAIN and LAYER active, use the FC7 to control VOLUME of the LAYER... while the MAIN Part is set to ignore VOLUME messages. This can be accomplished with the RECEIVE SWITCH - which allows you to set which PARTs follow which controllers.

The FC7 (continuous) pedal will be better for this than the FS (Foot Switch) Yamaha FS are always momentary, which would mean you would need to keep your foot on it to have it ON, when you released it it would turn OFF.

I'm not near my CP4 Stage now, there may be some other options ('tricks') I will revisit this question on Friday.

A continuous controller like the FC7 offers the most control, of course. But there is a way to use a footswitch with an expression pedal input jack on the CP4.

See my explanation here:
https://yamahasynth.com/index.php?option=com_easydiscuss&view=post&id=2184&Itemid=851#reply-2213

Just apply that to layer volume rather than Leslie speed and you get what you want, though it uses up one of the continuous foot pedal controller jacks for a switch. If you use at most one expression pedal that won't be an issue.

Note the part about using a latching footswitch, which is what you'd need for your application (unless it's OK that you'd to have to leave your foot on the switch whenever you want to hear the Layer part.)