Thank you for taking the time to post and welcome to the Bose Community. I hope you're enjoying your SoundTouch Wave system so far!
In regard to using wireless headphones with the system, this isn't possible with the Wave or through the SoundTouch app. As you've suggested, you'll likely need to connect a third-party Bluetooth transmitter to the AUX port of the system and connect through this way. However, this isn't recommended as we cannot account for the performance and compatibility of third-party devices.
However, you're more than welcome to give this a try if this would be what you prefer. Do let us know what you find, or if you have any further queries regarding your Wave system.
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