Stream Qobuz on Oppo BDP105

You could take the elcheapo route for now.
Google Chromecast Audio mini streamer ( still around $50 on eBay).
This in conjunction with bubbleupnp on an Android device will get you streaming Qobuz.

Or if your rig can use Bluetooth you could just install Qobuz app on your phone or tablet and stream direct from that to your bt enabled rig.
the Oppo is not going to work for Qobuz unfortunately.

Does Chromecast support 24-bit/192kHz streaming? I love my Oppo 105 with the Modwright tube modifications, so I'd rather keep it. I don't need a streamer that has its own DAC or storage, but I guess I could buy a Bluesound Node and bypass its internal DAC.

The Chromecast only supports up to 24/96.
The Node will do 24/192 on coax output I am sure but not so sure on the toslink?
What digital inputs does the 105 have or would you be needing to bring signal in via stereo RCA analog inputs?