Sorry, you need to use your iPhone as it offers the needed application, there is not Watch App under either the iPad or Mac systems.
Now, even still there is a hidden port on the watch where you can interface via a physical connection Vs Bluetooth/WiFi one normally accesses the watch once you’ve tied it to your iPhone. If you take off the strap you can see the small cover in the well. But you do need the special interface to gain access.
From what you describe it sounds like the iPhone it’s linked to is not available as it’s trying to get the files from it.