Not sure I understand your statement regarding Control Panel and "registered" programs. What I can say is the approach I took after researching this very annoying problem for months and following...

I tried all the same general and obvious answers that did not work, but finally I figured it out. You may want to try the solution I found - after months of searching and testing various approaches....

OK, this issue has been dogging me since I upgraded to Win 10.

As described above, Outlook 2013 and other apps were asking me each and every time I clicked on a link to choose a default browser...