Why don't you want to use Unity?
All you'd need to do is add a scene to the start that presents a menu of screen resolution choices for the user to select. Essentially building your own startup dialog. It means you can use screen.resolutions and playerPrefs to save the choices made, so you can auto-highlight/select them the next time the user plays your game. The size of the menu is dictated by the 'player' size you specify in player settings so it doesn't have to be full screen etc.
The alternative is far more complex as you'll have to write your own dialog 'app' using c++, VB or some other language, look up OS methods for getting valid screen resolutions, make a Win/Mac version etc.
Honestly unless you have some specific need, doing this outside of Unity just doesn't make any sense.