Alas, there are few other good candidates. Davis had been an exemplary Secretary of War, and was known and respected in both North and South as a liberal and an honest man. He has the reputation and the manners to be accepted by Virginia, which had not yet seceded. Breckinridge probably would have made a tolerable President, but he drank an exceptional amount, spit tobacco on the floor and spoke with a thick rural Kentucky accent; he was the backwoods southern lawyer to complement Buchanan the northern diplomat on the '56 ticket.
Toombs is probably as good as we can do. Stephens is rather too young and too cranky; among other things, he would not have passed a conscription law, which probably would have made the CSA collapse quickly indeed. But in order to bypass Davis, you probably need to dispose of him; he is clearly the best candidate, a President must be selected before generals, and one simply does not decline an offer of a Presidency.
Say Toombs does get selected. Does Virginia then secede, and merely recognize the Confederacy and attempt to exchange ambassadors?
Suppose they nominated Hughes of Virginia? Would he have accepted the position even though his state was still nominally part of the Union?
