Who Else but Lincooln?
With the Democratic Party split, a Republican victory was (almost) a given. If not Lincoln, it most probably would have been Seward,(although it is possible his victory may have been only by a plurality).
A foreign war to help unite the country would be such an obvious political ploy (and was well known to Washington insiders) to help keep the south in the union, that it is doubtful that it would have persuaded Seward's own party, much less the southern leaders or the British gov't (whatever, their publics may have thought).
Seward did not want to fight at Sumpter 'Because' it Was doomed to fall no matter what the inadequate forces available at that time, were employed. He wanted the Union stand to be made at Ft. Pickens at Pensacola, easily reinforced and supplied from the sea; thus entering the war with a signal victory at its very outset.
Seward was a professional politician (with all the faults and virtues that phrase conjures up), who worked within the system (like Lincoln). He was Union all the way, and although not so rock solid in the higher plains of Political Thought and Morality, he would have been stubborn in giving up the war for the Union. The advantages of the north, available to Lincoln was there for any other President and they were so overwhelming that even a President of modest ability would probably have been successful as Lincoln, (in a longer run, probably).
It is likely, that Seward (politican, that he was) and the radicals (opportunists, that they wer) could (or would) have come to an accomodation, which would likely have ended up freeing the slaves And IF Seward was not assasinated in Lincoln's stead, could have softened or eliminated the southern reactionary movement after reconstruction.
It May have taken a little longer and been a little harder fought, but the North under Seward would probably have prevailed, in any event.