Dawson is on trial accused of one count of carnal knowledge as a teacher of a girl aged between 10 and 17.
The 74-year-old will be given frequent breaks during the trial due to health issues in his older age.
He was jailed in 2022 for murdering his wife Lynette in January 1982, with a judge finding he was motivated by a desire to pursue an unfettered relationship with one of his students.
Public defender Claire Wasley asked on Monday for the NSW District Court to restrict what media can report during the trial to avoid contaminating witnesses yet to give evidence.
There has been too much media attention and even witnesses seeking to avoid news on the trial would be exposed to information, she said.
"And they would turn it off," Judge Sarah Huggett responded.
"That's what they're told to do. Jurors are told that … we trust jurors to do that."
Barrister Dauid Sibtain SC, arguing on behalf of several media organisations, said there was no evidence Ms Wasley's concerns would eventuate and there was no reason to treat the trial differently from any other.
"It is a general apprehension as opposed to evidence of a risk," he said.
The judge did not make specific orders, noting statutory laws already protect complainants from being identified in cases of alleged sexual offending.
"She will be known in this trial as AB and she will be identified as AB," Judge Huggett said of the complainant in this case.
She also noted there is no jury for the trial and many of the issues parties to the case sought to have suppressed are already widely known publicly.
"The horse has already bolted so to speak," Judge Huggett said as lawyers argued before her.
Dawson appeared in prison greens sitting in the dock for the judge-alone trial.
Crown and defence opening addresses are expected to commence on Tuesday.
The court will be closed for portions of the complainant's evidence, which will be given via audiovisual link.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
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