Why does 'clear defaults' not help? If the reason is that the app you want to use doesn't appear in the list then you won't be able to fix it that way.
The way it works is that when you click on a file your file browser broadcasts the 'intent' to open a file of this type. The OS will then have a list of apps that have declared themselves able to handle that intent. If there is only one, that app will be invoked to open the file. If one app has been declared the default for that intent it will be used. If no default is set then you are presented with a list of all apps declaring that they can handle it. If an app isn't on that list, it means that it has not subscribed to receive that type of request. In that case telling the OS to direct the intent to that app wouldn't work: you'd just find that clicking on the file did nothing.
An analogy I've heard is that a group of people interested in doing a job sign up to a mailing list. Someone wants to give a job to one of them, so uses the subject line 'FAO Peter'. Then Peter knows the message is for him and everyone else ignores it. But if Paul is not a member of the list, putting 'FAO Paul' as the subject won't get the message to him.
So if I've guessed right and that is your problem, you will need to contact the app developer and ask them to add this functionality. Or else launch the app first and then use it to select and open the file.
If I've guessed wrong and you actually want to for example write an app like Default App Manager yourself, apologies for wasting your time. But in that case to answer your last question, no you won't be able to see or alter any system settings database manually without root.