Please give this evidence for the Historical Jesus. Lots of writers with those two words in the Title of their books may be interested in your offerings.
You know, Josephus' works were definitely open to redaction. One version notes that Jerusalem fell five years before the last deportation and another just four years. So someone is making their own corrections of his work. The Bible indicates that Jerusalem fell in year 19 and the last deportation was year 23, so the 4-year reference was likely the original reference.
Josephus, though, knew quite well about the revisions of the NB Period and provided the original length of reign for Ewil-Merodach at Ant. 10.11.2:
When Evil-Mcrodach was dead, after a reign of eighteen years, Niglissar his son took the government,
There is a 26-year difference between the secular records from the Persian Period and the Bible/Josephus. We know from the Bible that Nebuchadnezzar II ruled for 45 years rather than just 43, so that takes care of 2 years. We also know directly from the Bible that Darius the Mede ruled for a full 6 years before abdicating to Cyrus; that amounts to 8 years. So there are 18 more years to make up for. We can calculate by deduction that Nabonidus ruled for 19 years instead of 17 years because the period from year 6 to the first of Cyrus is a period of 20 years. Darius the Mede ruled for 6 years so that leaves 14 years + 5 which is 19 years. So that takes care of 10 years of the 26, leaving 16 years elsewhere. Evil-Merodach is only accorded 2 years of rule so if you add the 16 years to his rule then he would have ruled for 18 years, which is precisely how long Josephus is claiming he ruled in this instance. Later on, of course, in Against Apion, this changes to just 2 years. So there is plenty of evidence for redactions.
So you have to look at each reference, I suppose.
In the meantime, I don't think there is any secular records that survive that would directly give us a historical confirmation for Jesus. But, who is to say the Jews along the way didn't destroy some of those records? They deny the Christ. So we can't say some actual records were not suppressed or destroyed.
Case in point, is the year of Jesus' birth in 2 BC. This contradicts the popular dating for the death of Herod in 4 BC based spuriously on an eclipse event mentioned by Josephus. In the meantime, Josephus plays both sides of the fence when it comes to Herod because the length of Herod's rule was reduced by 3 years and added to the reign of his son, Archaleus. The Bible notes that a census was taken when Quirinius was first governor over Judea, meaning that he was governor twice. But Roman records show him governor only once though for the period of 3-1 BC who was governor is left blank! So who is suppressing that information? Obviously, the governor between 3-1 BC was none other than Quirinius!
So while that is not directly showing the "historicity" of Jesus, it does show agreement with Herod ruling at the same time Quirinius was governor in 2 BC when a census was taken. Quirinius became governor again in 7 AD and took another census over which there was some controversy.
So, while Jesus might not have any direct "historicity," some of the things people point to that are considered contradictions to what history we do have, such as the census by Quirinius are now being cleared up that adds validity to the accuracy of the gospels. Here's a youtube video which shows where the governorships are all listed except for that critical period of 1-3 BC. This would suggest that if there was some historical reference in the secular records, it likely and could easily have been suppressed by anyone who did not want to expose the revisionism or the historicity of Christ.
http://www.youtube.com/watch?v=TepIl6_CkTY
Of course, a general rule of thumb is that most secular records that survive are war-oriented. When blood is spilled, people set up a monument. That combined with those destroying records. Case in point, the rule of Solomon. Nothing really survives about him specifically. But the invasion during his reign by Shishak survives in Egyptian records. The time of Solomon was one of peace, so not much is said. Later, we have the confrontation at Karkar in Assyrian records, subjugation of King Jehu kneeling before Shalmaneser and references to various other kings like Hezekiah and Jehoiachin in Assyrian and Babylonian records. Thing is, some people who find no corroborating records in the secular records presume that's a reason to doubt the biblical record, when it is not! Just because you have no surviving records in China or in Compton that mention Jesus doesn't mean he never existed or everything the gospels claim he did didn't happen. Thus while you may not be able to confirm the historicity of Jesus beyond the gospels, you can't disprove him either. It has to be a matter of faith.
But the second coming occurred on December 25, 1992 and the elect are seeing modern miracles, so the historicity of Jesus is a moot point now.