Hi, does DOpus have an option to hide the file-extension only for a specific file-type? (In System File Types)
No it doesn't.
Do you think such a (system-wide) option would be technically possible?
Technically, sure.
Very short answers ...
Sorry, Seemed that was what you were asking. If you intended to make a feature request rather than ask if a feature was possible then use the gpsoftware support form. (I'm replying from my phone so don't have the link handy.)