Guessathlon
The sport I have in mind, whilst requiring real athletes, I think would truly be just as comical. Essentially it is a guessing competition, each country willing to compete must send in two or more athletes, with the correct skills for one particular event. For example, one country might send in seven Olympic level netballers, the catch is however that no one knows which sport is going to be chosen until the event. Therefore, you may have five pro wrestlers attempting a swimming race, or two gymnasts attempting a horse-riding race.
Equipment would of course be provided to the participants however it is unlikely they would be trained in the specific sport.
Of course, you could do this with non-athletes however, athletes who specialise in certain areas, might be even more amusing.
And of course, you may get a scenario where the sport picked is say a team sport, such as netball and one country sent in only two athletes, technically they would still have to play, which would be rather interesting to watch.
Of course, athletes would have the option to opt out, but then they'd be missing out on the fun. Heh.