I have no experience with AirPlay speakers-- or for that matter with any wireless speakers-- so I have questions.
Does the sound need to be streamed from an Apple device? Is that how you're thinking of setting it up-- run the CP40's audio to a Mac, MacBook, iPad, iPhone, or other Apple device via a wired connection of some kind, then from there transmit it via AirPlay to the speakers? If so, I assume that would work, but I'm wondering if there will be any issues with latency.
I know that latency can be a problem with Bluetooth, but I know nothing about AirPlay and latency. Note that the impact of latency varies depending on whether you're streaming something (audio, video, both, or other data) that can be buffered and delayed as long as necessary to ensure an uninterrupted stream of data, versus a situation where the data needs to be as close to "live" as possible. Something that would be ideal for streaming recorded music might be a nightmare to try to use for steaming a live performance where any delay between playing a key and hearing the sound produced by that key could completely throw off your timing.
If you're going to have to use a wired connection coming from the CP40-- connected either to the headphones jack or to the separate L and R jacks-- would it be possible to just stick with the wires and connect directly to a small set of speakers, like computer speakers? I know you said the house isn't big enough for using your amp, but if it's big enough for AirPlay speakers then is it big enough for standard computer speakers, or would the length needed for the wires to reach the speakers be an issue?
Anyway, if you can run the audio from the keyboard to your Mac, MacBook, iPad, or whatever, then you could use AirPlay to broadcast it to the speakers; I just don't have any experience with doing that. As for how to connect, I'd probably go with something like the IK Multimedia iRig Pro Duo I/O. I'm not saying that would be the best option, as I honestly don't know-- but a lot of those small audio interfaces for iOS seem to have just a single mono input, whereas the iRig Pro Duo I/O has two mono inputs, hence you'd be able to connect the CP40's L and R outputs.