I actually do need to do more research onto who would be a worse Democratic candidate. Clark was more or less a last second place holder. I can assure you that the Prohibition Party win was a very close win and that it is a one time thing.
About the weakest would probably be Oscar Underwood.
However, it doesn't really matter, as even the poorest so far, Alton B Parker in 1904, still garnered nearly 38% of the vote, and none of the 1912 Dem hopefuls is remotely likely to go lower than that. The party is "on a roll" and the choice of candidate is likely to be only worth a couple of percentage points one way or the other. So the Democrats walk away with it, pretty much regardless of whom they nominate.
They are in essentially the same position as the Republicans will be in 1920. The other side is so weak that they could nominate unpledged Electors and the people would vote for them and let them choose whoever they want for POTUS. It was one of those years when the out party could nominate a dead dog and still win.