I'm pretty sure that Ranma knows better than to anger more than one fiancee at the same time, so he'll be a good boy if they get firm enough with him.
Okay, so are we able to come to an agreement on:
1. The competition takes place at the beach after an argument commences between Ukyo and Akane while the two of them are there with Ranma (like, Ranma and Akane are there with the family and Ukyo is there vending her Okonomiyaki or something.)
2. The competition is Ukyo's idea since Akane would never suggest such a thing, she might only let her jealousy of Ranma allow her to decide to participate, especially if it's just between her and one other fiancee.
3. The competition is held in a more secluded area of the beach courtesy of a distraction caused by Happosai and/or some sort of event that gets everyone else's attention.
That's pretty much all we need for the set-up. Other than that, Mad's idea can take place whenever, and that leaves things open for others who might want to join and jump in, possible as Shampoo or something.