Instead of using the control panel, find a file of the appropriate type, then right-click > Open With > Choose Default Program.
The UI that appears is similar, but has more options, including the ability to browse for an exe.
(Scroll to the bottom, if what you want is not not already in the list, and choose More Apps. Then scroll to the bottom again, if it's still not in the list, and choose Look for another app on this PC. Then you get a file browser. At least, that is how it works in Windows 10 on 14 Dec 2016. MS keep changing this UI so it may be different tomorrow. After choosing the program for one file type, it should then be in the list for others, and for me at least it appears in the control panel as well.)