The three Soviet Embassy officials/KGB officers who say they met Oswald when he went to Mexico City to go to Cuba said he was acting "nervously" and "shaking" at the time. Recall that the Cubans (Sylvia Duran) told Oswald that she needed to see his Soviet visa before she would give him a transit visa to go to Cuba. If he couldn't show one he would have to wait several months for the application to be processed. So he visited the Soviet embassy twice to get one.
Here is how they described him (this is from the Frontline special "Who was Lee Harvey Oswald?"):
FRONTLINE NARRATOR: At the Soviet embassy, he [i.e., Oswald] met with three consular officials. In fact, all three were KGB officers working under diplomatic cover. In this, their first interview, they recall that Oswald's hands were shaking and his behavior was erratic.
OLEG NECHIPORENKO, KGB: [through interpreter] We all thought the man had an unstable nervous system. He was extremely agitated.
VALERY KOSTIKOV, KGB: [through interpreter] During our talk, Oswald kept feeling in his pockets, taking out all sorts of papers. Then he took out a gun and put it in front of him. I sat opposite him. I took the gun away and put it on Pavel's desk.
Pavel Antonovich asked him, "Why did you come here with a gun? What do you need a gun for?" He said, "I'm afraid of the FBI. I'm being persecuted. I need a gun to protect myself, for my personal safety." That's what he said."
Okay, so he's acting in a desperate manner in order to get the visa from the Soviets. He says the "notorious FBI" is after him and that is why he needed the gun. So he is trying to persuade them that his life is in danger. But the reported shaking and nervousness were caused by? Oswald was known to be demanding but he was also usually cool and in command.
The three KGB officers are shown below. They were shown the photo of the reported "impostor" and all said the man was not the person who said he was Oswald. They said the man who identified himself as Lee Oswald was the actual Oswald.
The video of their interview is here: go to the 1:10:30 mark to see the above:
https://www.pbs.org/video/frontline-who-was-lee-harvey-oswald/