Looking for history of witch trials in general, in which I would hypothetically be able to convince those in the trial to give my innocence, through accounts of those who were able to do so. such trials elsewhere in the world where witch trials were present is also welcome.
This answer depends on what time during the witch trials. You're probably referring to the June-October 1692 trials since those included the executions. After October, a legal change made it so nearly everyone was found innocent for a lack of evidence. Let's go chronologically through the accusations, trials, and executions.
In February-May 1692, many people (mostly young girls but also older women and some men) made accusations of witchcraft. Dozens of people were arrested at an escalating rate. Richard Latner has some interesting analysis of this here- https://www.tulane.edu/~salem/Accusation%20Discussion.html
These accusations needed to persuade people that a person signed a deal with the devil, breaking their covenant with God and joining Satan. The afflicted victims would claim specters of people harmed them. This was called spectral evidence. The specter is the supernatural image of a person that the witch sends of themselves, often from a far distance of their physical person to enact harm on someone. Only those suffering from witchcraft saw these specters. For example, Ann Putnam Jr. claimed Rebecca Nurse harmed her and fellow victim Mercy Lewis saw Rebecca Nurse's specter in the room as well, but no one else sees Nurse. However, everyone did see the girls acting as if Nurse was attacking them. A lot of court documents with testimony that included this type of narrative can be found at salem.lib.virginia.edu
When the specter was seen, it was considered proof that the person was a witch who joined the devil. Sarah Osborne challenged this idea on March 1, 1692 at her examination by arguing the devil could impersonate an innocent person, but nearly all arguments in support of this were overlooked. Essentially you were arrested when the accusers saw your specter and if your specter was seen, you were a witch.
A number of accused witches realized the problem. If you cannot argue that you are not guilty, there were few options. The trials began in June 1692 and continued through October for the first phase. All those who went to trial previously plead their innocence during the examinations. This includes Samuel Wardwell who originally confessed but recanted. Many suspects confessed knowing it would delay their trial. Confessions started to appear in March and continued throughout the trials. By confessing, suspects were not saving their lives, but delaying their trial. The court used confessors to testify against accused witches who did not confess. As far as anyone knew, confessing did not save your life, but it provided time.
There is an exception. Rebecca Nurse claimed her innocence. Two confessors Deliverance and her daughter Abigail Hobbes testified against Nurse. However, Nurse questioned having the Hobbes women present since they were "of our company" meaning fellow prisoners were not legal evidence against a prisoner. The trial continued, and the jury found Nurse not guilty. But the judges wondered what she meant by her "company". Did Nurse inadvertently confess by referring to herself as company of these witches? The judges asked a few follow up questions, but the 70 year old Nurse was hard of hearing and did not respond to the questions she never heard. The jury reconvened and took it as evidence of her guilt, condemning her to hang on July 19, 1692.
Elizabeth Procter was able to delay her death sentence after being found guilty due to pregnancy. The Puritans believed that the soul of the unborn child committed no sin, so the execution of the mother needed to wait until after the birth. Her husband John Procter hanged on August 19, 1692. Elizabeth's death sentence was reprieved in December 1692 and she survived based on the legal change in October 1692.
This process of spectral evidence continued without question. By September 1692, most suspects understood that confessing saved you from execution for the time being. Mary Easty, the sister of Rebecca Nurse, petitioned Gov. William Phips to stop the trials. Easty wrote that she knew her accusation was a death sentence, she knew she could confess to save herself but would sin by telling a lie, and she accepted that she will hang, but asked to let "no more innocent blood be shed". Easty hanged on September 22, 1692.
In October, this all stopped. 19 people hanged by that point, and criticism of the trials grew to a point where the governor could not ignore it (and rumor that his wife Mary Phips was accused spread through Boston at the same time). The trials paused to figure out how to proceed and decided that spectral evidence was not legal. The trials resumed in January 1693, but without spectral evidence, there was no evidence to convict anyone of witchcraft. Those already condemned had their sentences lifted. Three suspects were convicted in 1693, but the governor granted them reprieves as well. However, Lydia Dustin after being found not guilty died in jail waiting to pay her jail fees for her release in March 1693.
In theory, there were ways to be found innocence. An upstanding church member like Rebecca Nurse with a large group of supporters signing petitions on her behalf nearly saved her life. But in reality, there was nothing you could do. If the governor had not intervened, those who confessed would probably have been executed as well at a later date. The best option you had was to buy time, and it worked for many people. After being released from jail, many people were impoverished from losing money due to Sheriff George Corwin's looting, reputations were damaged although most of the colony realized quickly what a mistake and tragedy occurred, and a lot of people moved away from Salem and Essex County. Emerson Baker discusses the Salem diaspora in his book A Storm of Witchcraft.