Office applications have used DDE (Dynamic Data Exchange) for a while for most inter-MSOffice communication. It is unlikely this will change in a future version.
DDE enables many of the advanced cross-application functionality within Office, and I don't believe system protocol handlers even begin to be capable of the functions DDE offers.
Assuming you're dealing with the "Send to OneNote" button in Outlook or other Office products, this is not looking for the handler for the various OneNote file types. Instead, it is packaging the data from the source content and then sending this data to OneNote directly, no need to check for protocol or file handler settings.
In fact, the Send to OneNote button in Office products cannot be reprogrammed either. It is a plugin, applied BY the installation of OneNote for Office. Uninstall OneNote from your Office install, and this plugin and button goes away.
To put it bluntly: The Send to OneNote button in Office products will only EVER send to the Office version of OneNote.
This means that your solution is to create a new button. It should be rather simple, actually. You just need a button that triggers a print job and sends to the Print To OneNote function, and then make sure the app version of OneNote is the default OneNote application.