I strongly suspect that Ugarte left the letters of transit with Mr. Blaine. I would suggest you search the cafe immediately and thoroughly.
If Rick has the letters, he's much too smart to let you find them there.
You give him credit for too much cleverness. My impression was that he's just another blundering American.
But we mustn't underestimate American blundering. I was with them when they blundered into Berlin in 1918.