Every dance needs both steps and technique. The technique is often much harder to learn and requires a lot more time for you to look good. I believe that your best bet would be a dance that permits the technique to be minimized or faked. To me, that means Rhumba. It is slow enough to be non-stressful, the technique requirements can be faked for a short dance, and everyone should be looking at the girl anyway (that means YOU). The steps are not hard, the box step in particular is an easy "thinking" step (... what am I supposed to do next?), and if your fiance looks hungrily enough at you, it is entirely in keeping with the spirit of the dance.
Jerry