The February 2022 crash killed Wright's friend and Outback Wrangler TV show co-star Chris "Willow" Wilson, who was hanging from a sling under the chopper on a mission to collect crocodile eggs.
A jury was set to be chosen on Thursday.
But in the Supreme Court in Darwin on Wednesday, Acting Justice Allan Blow rescheduled the empanelment for August 5.
It ensures the jury will be selected following a long weekend, with August 4 marking the Picnic Day public holiday in the territory.
The start of the trial has been delayed several times and pre-trial legal argument before Justice Blow is set to continue this week.
On Monday Wright pleaded not guilty to three counts of attempting to pervert the course of justice, accused of tampering with evidence to cover up non-adherence to aircraft maintenance rules.
The trial is expected to take up to four weeks and hear from about 25 witnesses.
An Australian Transport Safety Bureau report into the crash near the King River in Arnhem Land found the chopper's engine stopped mid-flight because of a lack of fuel.
The crash into a paperbark swamp killed Mr Wilson, 34, and critically injured pilot Sebastian Robinson, 28.
The charge of attempting to pervert the course of justice carries a maximum 15-year jail term in the NT.
Wright rose to fame starring in National Geographic's Outback Wrangler and Netflix series Wild Croc Territory.
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