AMC1 FCL.235 Skill test contains all the requirements for the PPL Skill Test. It makes no mention of controlled or uncontolled aerodromes so the route is up to the Examiner.
The route to be flown for the navigation test should be chosen by the FE. The route may end at
the aerodrome of departure or at another aerodrome.
The diversion does not even need to be an aerodrome, a suitable point on the map can be assumed to be a grass landing strip.