Hello Graham
It makes little sense to take the IC, as you will have to change to the IR service at Arth-Goldau, or at Erstfeld (latest). Therefore, I suggest you to use the IR46 from Zurich. For IR trains, a reservation is not possible; bicycles will be transported if space is available (no guarantee). Same for the trains from Göschenen to Oberalp Pass via Andermatt, operated by Matterhorn Gotthard Bahn.
Expect a high number of bicycles if you travel on a Sunday morning, especially with good weather. Whenever you can, travel in the afternoon.
Kind regards,
Roland