Love a slightly droopy nose - would a supratip break during surgery be the best option?

A supratip break gives definition to the tip of the nose and the creation of one may create a slight lift to the tip, or at least the illusion thereof. Therefore, that would be counter to what you seek with a tip that drops, particularly with smiling.
You may want to consider Botox (or similar) to some of the nasalis musculature if these muscles, in you, are particularly strong at elevation of your nose with smiling. Weakening them, if that's your situation, may produce the desired result.

A full set of facial photographs are required to make a determination about how best to proceed. Digital computer imaging would be helpful in the education process for you to understand what can and cannot be accomplished with the procedure. In our practice, we usually give it a supratip break, and we release the depressor septi ligament which dynamically pulls the tip downward when smiling.