Paul McIntyre, 52, of Kinnego Park, is charged with the murder of Ms McKee, possessing a firearm with intent and belonging to a proscribed organisation.
He is further charged, along with Christopher Gillen, 39, of Balbane Pass, with petrol bomb offences.
Both men also face hijacking, arson and rioting charges.
The court had initially pencilled in a possible date of Tuesday, September 1, for Committal proceedings.
Both men deny the charges against them.
Ms McKee, 29, was observing rioting in Derry’s Creggan estate when she was shot on 18 April 2019.
He said that while the courts were being “phased back in”, a hearing on disclosure would still present problems with finding a court room big enough.
The case was adjourned until September 1 to deal with the disclosure issues.