Say I am physically out-of-shape, but I want to be an Olympian. What should I go for?
I’m guessing the coxswain.
But you gotta be a little guy.
Probably one of the shooting events.
I think they should transform these into a biathlon, where they run a mile, then shoot, then run a mile, shoot, etc. Then, it may not be best for you.
Most coxes are pretty fit, they generally work out with the teams during dryland training. I would guess archers, shooters, and curlers.
Don’t know if you knew this, but the Modern Pentathlon already works that way.
Shooting for sure.
I guess you didn’t see the Canadian men’s curling team in 2014. They looked like decathletes.
Out of shape curlers don’t cut it anymore in top competition. If you don’t have arm and core strength, you lack control.
How about equestrian?
A good way to end this debate once and for all would be to make darts an Olympic sport. 
Not easy to control a horse, but I suspect it’s an event where age and guile come into play. Patience, too.
Darts would be a great Olympic sport - perfect for TV. The crowd has got to be pissed, raucous and in fancy dress though
Ooooh…and that was a bad miss.
Golf
Coxswain here.
This is not the answer.
And there is that guy with the big tattoo on the side of his head…
Which? Little guy or fitness?
I’m sure fitness, as all the coxswains I’ve known are pretty darn fit - they train with the rowers.
But the OP was asking least fit. I can’t imagine a cox needs to have Olympic rower level fitness.
Though I could be wrong. Won’t be the first time.
Define fit-
Muscle vs fat
Aerobic capacity/endurance
Flexibility
Strength
Etc.
I’m guessing Dionysus, if you count him. He seems to be mostly slacking off and drinking wine. Otherwise… Aphrodite? She’s more about natural beauty than being a fitness freak.
Apologies if you didn’t mean that kind of Olympian.