We’re glad you asked, @seanr83! The best way to transfer an Alarm to another person, is indeed to remove and unregister the Alarm devices. To start, please remove each Alarm device from the Base Station first. This help center article will help and, although it is titled for the Motion Detector, it will contain similar steps necessary for removing all of the Alarm devices.
Once you are left with nothing but the Base Station in the Ring app, please unregister that Base Station. This help center article has instructions on how to do so.
While it will likely not be necessary, it is good to keep our Change of Ownership process in mind, in case the new owners still need gain access for any reason. After completing the steps above, the Alarm should allow the new owners to set it up quickly and easily in their Ring app. I hope this helps!