Rakuraku carried out the murder using a taiaha.
He buried his victim in a shallow grave near Eskdale in 2011.
During the jury trial in 2014, he admitted burying Mr Wright out of panic, but denied having anything to do with his death.
Rakuraku represented himself during a three-week trial at the High Court in Napier.
He will represent himself again at his appeal hearing.
Mr Wright's brother Paul Wright said they were shocked Rakuraku was continuing to deny his involvement.
"We waited for so long to actually get to court and then the horrifficness of the whole process, his general behaviour was hideous and now it's all happening again."
He said Rakuraku's appeal will retraumatise the family.
"We started moving on and had dealt with a lot of the grief and horrifficness that happened with Johnny's murder and it just took us back to day one," Mr Wright said. "Mum and dad were absolutely devastated."
Detective Senior Sergeant Brent Greville, the officer in charge of the murder investigation, said he felt sorry for the Wright family because the court process hasn't been finalised yet.