Instead of Edward Everett, who was more popular in the North, Sam Houston would have been more popular in the Slave states (especially the western ones). His popularity in Texas would probably let Bell win that state and it would give Bell the extra .2% needed to win Missouri. Most of the votes, except from Texas, mostly would have come from Douglas I suppose.
Therefore, at worst, I think the map would look like this:
If Sam Houston proves popular enough, I think other could could have been conceivably flipped as well. They could be: .8% for Maryland, 4.9 for Louisiana (which had 15.1% voting for Douglas), and possibly even 3.8% for North Carolina if they could take away enough votes from Breckenridge.
Therefore, at best, the map could look like this:
Personally, I hope a weak showing for the Democrats would have caused fewer states to succeed (such as Virginia or Texas). It would be a fascinating timeline.