When I hear the word slip it conjures up an image of an alcoholic trying to climb out of a muddy hole (the alcoholic pit) with slippery sides, using only his feet. There are hands (help) the he could grab, but he prefers self reliance. He makes a successful step or two but loses traction and slips back into the mud.
When I hear the word relapse I think of an alcoholic who has found a way out of the pit for a time, but goes back, gets too close to the edge and falls in. The first is just time between drinks, the second is from a position of recovery.
Anyway, if I was you, and I once was, I would keep AA till last. Give the CBT a good shot, and try anything else that comes to mind too. Something may work.
If nothing does, and you survive, you may find that AA looks a bit more attractive.