I didn\'t find an explicit answer to this question in the WiX Documentation (or Google, for that matter). Of course I could just write the appropriate registry keys in HKCR,
"If your application handles its own file data type, you will need to register a file association for it. Put a ProgId inside your component. FileId should refer to the Id attribute of the File element describing the file meant to handle the files of this extension. Note the exclamation mark: it will return the short path of the file instead of the long one:"
Reference: https://www.firegiant.com/wix/tutorial/getting-started/beyond-files/