This is an interesting question by a keen reader.
Bob's hand obviously trembled because he was experiencing a strong emotion, or a combination of emotions. O. Henry seems to be leaving it up to the reader to guess what emotions these were. No doubt, Bob was surprised, disappointed, angry, resentful, shocked, and frightened. We don't know exactly why he was wanted by the police in Chicago. It could have been for something so serious that he would be facing the death penalty or at least a long term in prison. O. Henry hints that Silky Bob is a confidence trickster, but he could have gotten into a situation that led to a more serious crime.
Bob tells Jimmy, whom he doesn't recognize:
"I've had to compete with some of the sharpest wits going to get my pile. A man gets in a groove in New York. It takes the West to put a razor-edge on him."
Such remarks suggest that Bob was living by his wits at some sort or racket and was not involved in anything that could lead to capital punishment. At the same time, they would suggest that Silky Bob's strongest emotion was caused by his realization that he, the slick, worlldly wise trickster, had been tricked himself, and tricked by a man he considered inferior to himself as far as cleverness and imagination were concerned.
"Did pretty well out West, didn't you?" asked the policeman.
"You bet! I hope Jimmy has done half as well. He was a kind of plodder, though, good fellow as he was."
Perhaps Bob's strongest emotion comes from his humiliating realization that he has been tricked twice, or even three times. Jimmy tricked him by not letting him know he was the cop Bob was bragging to about his sharp wits and his financial success. Jimmy tricked him again by finding out how long he planned to be standing there in the doorway.
"Going to call time on him sharp?"
"I should say not!" said the other. "I'll give him half an hour at least. If Jimmy is alive on earth he'll be here by that time. So long, officer."
Jimmy tricked him by getting a plain clothes officer to make the arrest in his place. The other officer tricked Bob by letting him think he was really Jimmy. Both officers were New Yorkers, and Bob had suggested that New York was a town for "plodders." Bob knew he was wanted in Chicago, but he thought he was too smart to be caught in New York.
No doubt, Bob is hurt by having an old friend turn against him as he did, but a lot can change after twenty years. Bob feels hurt because it was he himself who gave his identity away and who walked right into the arms of the New York City law. He must be feeling a whole gamut of emotions. He knows he is twenty years older, may lose all his money in legal fees or restitutions, and may never be able to regain his present affluent status.