That means the HDMI cable is sending out audio on a different set of pins than it comes in on, which makes things more challenging, and expensive, to my knowledge. You’d need another HDMI ARC to optical converter, something which isn’t standard with a normal HDMI switch.
The ones I’m familiar with are the HD Fury Arcana, the Feintech VAX04101k, and the OREI HDA-935. You can also order from those links from the companies directly, or check your local retailers for availability. Amazon may carry some, depending on location. At this point, there may be more manufacturers, I haven’t been keeping track.
On the other hand, I’ve not really investigated any optical outputs on these devices.
Since the Ray doesn’t do Dolby Atmos, I’d be awfully tempted to pull off the audio using a standard switch before the signal reaches the projector, and not after. Much less expensive, and you don’t need to worry about ARC stuff.