Finally got it to work (well I think so???) with a mixture of approaches.

Even though my Oracle home is correctly set in the registry, by setting the ORACLE_HOME system variable it seems that Opatch can see it!

I navigate to the folder where Opatch is (via the Command Prompt) and execute:

Opatch apply \patchfile

Opatch starts and echoes back very encouraging messages about Patching and Updating Inventory ... and then finishes with 'Opatch succeeded'.

So, where can I find evidence that the software has been patched? V$version still shows me 9.2.0.4.0