This is a two-part question, and I'm going to take each part separately.
1. Was Jesus a political revolutionary?
To answer this question, it's important to understand what politics meant in the context of the nations living under the shadow of the Roman Empire.
After the assassination of Julius Caesar, the Roman Senate had declared him to be a God, and dedicated a temple to him. Octavian, as his adopted son, took the title Divi filius ("Son of God"). After Octavian's victory in the Battle of Actium, ending Rome's long civil war, Octavian was given the title Augustus ("Majestic" or "Venerable").
Augustus believed himself to be not just the divinely appointed leader of Rome, but the man who would bring peace (through military conquest) to the whole world. For his efforts, Augustus was lauded as the savior of the world.
So when the early Christians proclaimed Jesus the "savior of the world" and the "son of God", they were not just making theological statements in a political vacuum. These statements were also a direct challenge to Augustus' authority. Jesus' claim of having his own kingdom (even though "not of this world") would also have been understood as a challenge to Rome's authority over all kingdoms.
So, when Jesus was crucified (the canonical example of the criterion of embarrassment, and also attested in Tacitus), the signs listing the charge against him said he was the "King of the Jews" (see Matthew 27:37 | Mark 15;26 | Luke 23:38 | John 19:19). This clearly indicates that his crime (from Rome's perspective) was political.
2. Was Jesus a violent revolutionary?
There are statements in the gospels that, read in isolation, could be taken as support for violent revolution. For example, Matthew 10:34-39:
Do not think that I have come to bring peace to the earth; I have not come to bring peace, but a sword. For I have come to set a man against his father, and a daughter against her mother, and a daughter-in-law against her mother-in-law; and one's foes will be members of one's own household. Whoever loves father or mother more than me is not worthy of me; and whoever loves son or daughter more than me is not worthy of me; and whoever does not take up the cross and follow me is not worthy of me. Those who find their life will lose it, and those who lose their life for my sake will find it.
Or Luke 22:35-36:
He said to them, "When I sent you out without a purse, bag, or sandals, did you lack anything?" They said, "No, not a thing." He said to them, "But now, the one who has a purse must take it, and likewise a bag. And the one who has no sword must sell his cloak and buy one."
But in the larger context of the gospels, Jesus' movement is portrayed as a nonviolent one. He will bring about change, not through bloodshed like the Romans, but through changing people's hearts and minds. I won't go into all the details here, since you're looking primarily for secular documentation.
The main reason, from a secular/historical point of view, to believe Jesus was not a violent revolutionary, is to look again at his crucifixion. Although Jesus was crucified as a political threat, his followers were not. That's important, because Josephus records a number of crucifixions of political revolutionaries. Every time subjects took up arms against Rome, survivors of the battle were crucified. This could run into the hundreds or thousands.
Here's an example from Antiquities 17.10.
Upon this, Varus sent a part of his army into the country, to seek out those that had been the authors of the revolt; and when they were discovered, he punished some of them that were most guilty, and some he dismissed: now the number of those that were crucified on this account were two thousand.
If the Romans had believed Jesus' followers were a threat, or were likely to challenge Rome on their own, the disciples would have been rounded up and crucified with him. Since they weren't, the evidence suggests that Jesus was seen by Rome as a nonviolent political revolutionary.