One of the effects of nicotine is stimulation of the prefrontal cortex. This is the area of the brain that is understimulated in people that have ADHD. RItalin and Adderall act similarly in the prefrontal cortex. Before you take nicotine that part of your brain is like Johnny 5 in Short Circuit: Need input!!!! You need something interesting/pleasurable to provide stimulation. So the nicotine is artificially creating the endorphin/neurotransmitter rush which results in the calming feeling.
I do not think this has any effect on cortisol. If anything the increased CNS effects such as rapid heartbeat and dilation of blood vessels would increase cortisol levels. I have seen studies that state that nicotine and tobacco alkaloids are a potent aromatase inhibitor. That would in theory support a claim that it elevates testosterone. But a cortisol-testosterone connection, I do not think there is a causal relationship between the two.