Likewise, you can use the digital audio output of the TV to the Bose system to get audio back into the Bose. Instead of switching inputs on the Bose, you would switch inputs on the TV to go to your different sources.
As well, this will allow you to feed your 4K TV 4K sources directly and get the full resolution that the TV allows for and just have audio into the Bose.
It's not as convenient, perhaps, but it does give you the best possible video which is nice based upon the age of your gear.
When you are ready to upgrade the Bose to a 4K capable A/V receiver, we can talk about why most people don't recommend Bose as a product.