I've not seen one, but if you can set the machine to play the sound you want upon powering up, you could add a HomeKit outlet switch to turn it on/off when desired. But if it won't play sound without tapping buttons after powered up, then that may not help.
I bought a white noise machine with a "dumb" power switch which will stay on even if the plug is unplugged and plugged back in. It is plugged into an iDevices switch so I can control it with Siri.